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1.

図書

図書
Robert Gilmore
出版情報: New York : Wiley, c1974  xx, 587 p. ; 23 cm
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2.

図書

図書
[by] J. Frank Adams
出版情報: New York : W.A. Benjamin, 1969  xii, 182 p. ; 23 cm
シリーズ名: Mathematics lecture note series
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3.

図書

図書
Nicolas Bourbaki
出版情報: Paris : Hermann , Reading, Mass. : Addison-Wesley, c1975-  v. ; 24 cm
シリーズ名: Actualités scientifiques et industrielles ; . Elements of mathematics
Adiwes international series in mathematics
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4.

図書

図書
Nolan R. Wallach
出版情報: Boston ; Tokyo : Academic Press, c1988-c1992  2 v. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 132, 132-2
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5.

図書

図書
Glen E. Bredon
出版情報: New York : Academic Press, 1972  xiii, 459 p. ; 23 cm
シリーズ名: Pure and applied mathematics ; v. 46
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6.

図書

図書
Norman Hurt and Robert Hermann
出版情報: Brookline, MA : Math Sci Press, [1980]-  v. <1 > ; 24 cm
シリーズ名: Lie groups : history, frontiers, and applications ; Vol. 10
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7.

図書

図書
[by] M.S. Raghunathan
出版情報: New York ; Berlin : Springer-Verlag, 1972  viii, 226 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; Bd. 68
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8.

図書

図書
by A. Borel and N. Wallach
出版情報: Princeton, N.J. : Princeton University Press , Tokyo : University of Tokyo Press, 1980  xvii, 387 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 94
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9.

図書

図書
Sigurdur Helgason
出版情報: New York : Academic Press, c1978  xv, 628 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 80
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目次情報: 続きを見る
Elementary Differential Geometry
Lie Groups and Lie Algebras
Structure of Semisimple Lie Algebras
Symmetric Spaces
Decomposition of Symmetric Spaces
Symmetric Spaces of the Noncompact Type
Symmetric Spaces of the Compact Type
Hermitian Symmetric Spaces
Structure of Semisimple Lie Groups
The Classification of Simple Lie Algebras and of Symmetric Spaces
Solutions to Exercises
Some Details
Bibliography
List of Notational Conventions
Symbols Frequently Used
Index
Elementary Differential Geometry
Lie Groups and Lie Algebras
Structure of Semisimple Lie Algebras
10.

図書

図書
Willard Miller, Jr.
出版情報: New York : Academic Press, 1972  x, 432 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 50
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11.

図書

図書
M. Scott Osborne and Garth Warner
出版情報: New York : Academic Press, 1981  xiii, 385 p. ; 24 cm
シリーズ名: Pure and applied mathematics : a series of monographs and textbooks ; 99
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12.

図書

図書
E.B. Dynkin ; A.A. Yushkevich, G.M. Seitz, A.L. Onishchik, editors
出版情報: Providence, R.I. : American Mathematical Society , Cambridge, Mass. : International Press, c2000  xxvi, 798 p. ; 27 cm
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Lie groups and Lie algebras: Dynkin and Lie theory / G. M. SeitzPart I:
On the work of E. B. Dynkin in the theory of Lie groups / F. I. Karpelevich ; A. L. Onishchik ; E. B. Vinberg
Correction to On the work of E. B. Dynkin in the theory of Lie groups
Classification of simple Lie groups / E. B. Dynkin
Calculation of the coefficients in the Campbell-Hausdorff formula
The maximal subgroups of the classical groups
Comments on Maximal subgroups of the classical groups
Semisimple subalgebras of semisimple Lie algebras
Comments on the paper Semisimple subalgebras of semisimple Lie algebras
Construction of primitive cycles in compact Lie groups
Topological characteristics of homomorphisms of compact Lie groups
Comments on the paper Topological characteristics of homomorphisms of compact Lie groups
Dynkin and modern Lie theory / B. Kostant
Comments on the impact of Dynkin's work on current research in representation theory / D. A. Vogan
Coxeter-Dynkin diagrams and singularities / A. Gabrielov
Lie groups in physics / K. Gottfried
Dynkin diagrams in the physics of particles, fields and strings / Y. Ne'eman
Probability theory: Dynkin and probability theory / A. A. YushkevichPart II:
Necessary and sufficient statistics for a family of probability distributions
Some limit theorems for sums of independent random variables with infinite mathematical expectations
Markov processes and semigroups of operators
Strong Markov processes
Infinitesimal operators of Markov processes
The natural topology and excessive functions connected with a Markov process
Random walk on groups with a finite number of generators / M. B. Malyutov
The optimum choice of the instant for stopping a Markov process
Brownian motion in certain symmetric spaces and nonnegative eigenfunctions of the Laplace-Beltrami operator
Diffusion of tensors
Game variant of a problem on optimal stopping
Determining functions of Markov processes and corresponding dual regular classes / S. E. Kuznetsov
Economic equilibrium under uncertainty
Comments on Economic equilibrium under uncertainty / I. V. Evstigneev
Markov processes and random fields
Green's and Dirichlet spaces associated with fine Markov processes
Markov processes as a tool in field theory
Symmetric statistics, Poisson point processes, and multiple Wiener integrals / A. Mandelbaum
Gaussian and non-Gaussian random fields associated with Markov processes
Author's correction to Guassian and non-Gaussian random fields associated with Markov processes.
An application of flows to time shift and time reversal in stochastic processes
Author's comments on An application of flows to time shift and time reversal in stochastic processes
Representation for functionals of superprocesses by multiple stochastic integrals, with applications to self-intersection local times
A probabilistic approach to one class of nonlinear differential equations
Superdiffusions and parabolic nonlinear differential equations
Comments on Superdiffusions and parabolic nonlinear differential equations
Dynkin and the theory of Markov processes / P. A. Meyer
To the history of strong Markov property
On compactifications of symmetric spaces / M. A. Olshanetsky
Dynkin's contributions to superprocesses and partial differential equations / J.-F. Le Gall
Dynkin's work in mathematical economics
Acknowledgments
Lie groups and Lie algebras: Dynkin and Lie theory / G. M. SeitzPart I:
On the work of E. B. Dynkin in the theory of Lie groups / F. I. Karpelevich ; A. L. Onishchik ; E. B. Vinberg
Correction to On the work of E. B. Dynkin in the theory of Lie groups
13.

図書

図書
W.Y. Hsiang
出版情報: Singapore : World Scientific, c2000  v, 108 p. ; 22 cm
シリーズ名: Series on university mathematics ; vol. 2
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14.

図書

図書
by Karl-Hermann Neeb
出版情報: Berlin : Walter de Gruyter, 2000, c1999  xxi, 778 p. ; 25 cm
シリーズ名: De Gruyter expositions in mathematics ; v. 28
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目次情報: 続きを見る
Preface
Introduction
Abstract Representation Theory / A.:
Reproducing Kernel Spaces / Chapter I.:
Operator-Valued Positive Definite Kernels / I.1.:
The Cone of Positive Definite Kernels / I.2.:
Representations of Involutive Semigroups / Chapter II.:
Involutive Semigroups / II.1.:
Bounded Representations / II.2.:
Hermitian Representations / II.3.:
Representations on Reproducing Kernel Spaces / II.4.:
Positive Definite Functions on Involutive Semigroups / Chapter III.:
Positive Definite Functions--the Discrete Case / III.1.:
Enveloping C*-algebras / III.2.:
Multiplicity Free Representations / III.3.:
Continuous and Holomorphic Representations / Chapter IV.:
Continuous Representations and Positive Definite Functions / IV.1.:
Holomorphic Representations of Involutive Semigroups / IV.2.:
Convex Geometry and Representations of Vector Spaces / B.:
Convex Sets and Convex Functions / Chapter V.:
Convex Sets and Cones / V.1.:
Finite Reflection Groups and Convex Sets / V.2.:
Convex Functions and Fenchel Duality / V.3.:
Laplace Transforms / V.4.:
The Characteristic Function of a Convex Set / V.5.:
Representations of Cones and Tubes / Chapter VI.:
Commutative Representation Theory / VI.1.:
Representations of Cones / VI.2.:
Holomorphic Representations of Tubes / VI.3.:
Realization of Cyclic Representations by Holomorphic Functions / VI.4.:
Holomorphic Extensions of Unitary Representations / VI.5.:
Convex Geometry of Lie Algebras / C.:
Convexity in Lie Algebras / Chapter VII.:
Compactly Embedded Cartan Subalgebras / VII.1.:
Root Decompositions / VII.2.:
Lie Algebras With Many Invariant Convex Sets / VII.3.:
Convexity Theorems and Their Applications / Chapter VIII.:
Admissible Coadjoint Orbits and Convexity Theorems / VIII.1.:
The Structure of Admissible Lie Algebras / VIII.2.:
Invariant Elliptic Cones in Lie Algebras / VIII.3.:
Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups / D.:
Unitary Highest Weight Representations: Algebraic Theory / Chapter IX.:
Generalized Highest Weight Representations / IX.1.:
Positive Complex Polarizations / IX.2.:
Highest Weight Modules of Finite-Dimensional Lie Algebras / IX.3.:
The Metaplectic Factorization / IX.4.:
Unitary Highest Weight Representations of Hermitian Lie Algebras / IX.5.:
Unitary Highest Weight Representations: Analytic Theory / Chapter X.:
The Convex Moment Set of a Unitary Representation / X.1.:
Irreducible Unitary Representations / X.2.:
The Metaplectic Representation and Its Applications / X.3.:
Special Properties of Unitary Highest Weight Representations / X.4.:
Moment Sets for C*-algebras / X.5.:
Moment Sets for Group Representations / X.6.:
Complex Ol'shanskii Semigroups and Their Representations / Chapter XI.:
Lawson's Theorem on Ol'shanskii Semigroups / XI.1.:
Holomorphic Extension of Unitary Representations / XI.2.:
Holomorphic Representations of Ol'shanskii Semigroups / XI.3.:
Irreducible Holomorphic Representations / XI.4.:
Gelfand-Raikov Theorems for Ol'shanskii Semigroups / XI.5.:
Decomposition and Characters of Holomorphic Representations / XI.6.:
Realization of Highest Weight Representations on Complex Domains / Chapter XII.:
The Structure of Groups of Harish-Chandra Type / XII.1.:
Representations of Groups of Harish-Chandra Type / XII.2.:
The Compression Semigroup and Its Representations / XII.3.:
Examples / XII.4.:
Hilbert Spaces of Square Integrable Holomorphic Functions / XII.5.:
Complex Geometry and Representation Theory / E.:
Complex and Convex Geometry of Complex Semigroups / Chapter XIII.:
Locally Convex Functions and Local Recession Cones / XIII.1.:
Invariant Convex Sets and Functions in Lie Algebras / XIII.2.:
Calculations in Low-Dimensional Cases / XIII.3.:
Biinvariant Plurisubharmonic Functions / XIII.4.:
Complex Semigroups and Stein Manifolds / XIII.5.:
Biinvariant Domains of Holomorphy / XIII.6.:
Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups / Chapter XIV.:
Biinvariant Hilbert Spaces / XIV.1.:
Hardy Spaces Defined by Sup-Norms / XIV.2.:
Hardy Spaces Defined by Square Integrability / XIV.3.:
The Fine Structure of Hardy Spaces / XIV.4.:
Coherent State Representations / Chapter XV.:
Complex Structures on Homogeneous Spaces / XV.1.:
Heisenberg's Uncertainty Principle and Coherent States / XV.2.:
Appendices
Bounded Operators on Hilbert Spaces / Appendix I.:
Spectral Measures and Unbounded Operators / Appendix II.:
Holomorphic Functions on Infinite-Dimensional Spaces / Appendix III.:
Symplectic Geometry / Appendix IV.:
Simple Modules of p-Length 2 / Appendix V.:
Symplectic Modules of Convex Type / Appendix VI.:
Square Integrable Representations of Locally Compact Groups / Appendix VII.:
The Stone-von Neumann-Mackey Theorem / Appendix VIII.:
Bibliography
List of Symbols
Index
Preface
Introduction
Abstract Representation Theory / A.:
15.

図書

図書
A.L. Onishchik, E.B. Vinberg (eds.)
出版情報: Berlin : Springer, c2000  223 p. ; 24 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 21 . Lie groups and Lie algebras ; 2
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16.

図書

図書
Lajos Pukánszky
出版情報: Providence, R.I. : American Mathematical Society, c1999  xvii, 128 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 71
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目次情報: 続きを見る
Unitary representations of locally algebraic groups
Unitary representations of elementary groups
Existence of characters
Generalized Kirillov theory
Bibliography
Unitary representations of locally algebraic groups
Unitary representations of elementary groups
Existence of characters
17.

図書

図書
Nail H. Ibragimov
出版情報: Chichester, West Sussex ; New York : Wiley, c1999  xviii, 347 p. ; 24 cm
シリーズ名: Mathematical methods in practice ; v. 4
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目次情報: 続きを見る
Introduction to Differential Equations
Transformation Groups
Lie Group Analysis of Ordinary Differential Equations
Brief on Lie Algebras
First Order Differential Equations
Integration of Second Order Equations
Basic Theory of Linear Equations
Nonlinear Second Order Equations
Integration of Third Order Equations
Nonlinear Superposition Principle
Index
Introduction to Differential Equations
Transformation Groups
Lie Group Analysis of Ordinary Differential Equations
18.

図書

図書
by Antonio Kumpera and Donald Spencer
出版情報: Princeton, N.J. : Princeton University Press , Tokyo : University of Tokyo Press, 1972  xv, 293 p. ; 24 cm
シリーズ名: Annals of mathematics studies ; no. 73 . Lie equations / by Antonio Kumpera and Donald Spencer ; v. 1
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19.

図書

図書
edited by B.P. Komrakov ... [et al.]
出版情報: Dordrecht ; Boston, Mass. : Kluwer Academic Publishers, c1998  vii, 442 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 433
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20.

図書

図書
Jean-Pierre Serre
出版情報: New York : W.A. Benjamin, c1965  1 v. (various pagings) ; 28 cm
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21.

図書

図書
J. Dieudonné
出版情報: New York : M. Dekker, 1973  xii, 265 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 20
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22.

図書

図書
by Boris Rosenfeld
出版情報: Dordrecht ; Boston : Kluwer, c1997  xviii, 393 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 393
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23.

図書

図書
R.S. Ismagilov ; [translated by D. Deart from an original Russian manuscript]
出版情報: Providence, R.I. : American Mathematical Society, c1996  x, 197 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 152
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目次情報: 続きを見る
Some general constructions related to representations
Representations of the group of measurable currents
Representations of the group of smooth currents
Certain results on diffeomorphism groups
Representations of diffeomorphism groups associated with configuration spaces
Representations of certain group extensions
Representations of diffeomorphism groups in the Fock space
Representations of groups of foliation preserving diffeomorphisms
References
Some general constructions related to representations
Representations of the group of measurable currents
Representations of the group of smooth currents
24.

図書

図書
edited by N.H. Ibragimov ... [et al.]
出版情報: Boca Raton, Fl. ; Tokyo : CRC Press, c1996  xvi, 536 p. ; 25 cm
シリーズ名: CRC handbook of Lie group analysis of differential equations / edited by N.H. Ibragimov ; v. 3
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25.

図書

図書
Roger Carter, Graeme Segal, Ian Macdonald
出版情報: Cambridge, UK ; New York : Cambridge University Press, 1995  viii, 190 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 32
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26.

図書

図書
editors, Karl H. Hofmann, Jimmie D. Lawson, Ernest B. Vinberg
出版情報: Berlin ; New York : Walter de Gruyter, 1995  xii, 370 p. ; 25 cm
シリーズ名: De Gruyter expositions in mathematics ; 20
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27.

図書

図書
J.F. Adams ; edited by Zafer Mahmud and Mamoru Mimura
出版情報: Chicago, Ill. : University of Chicago Press, 1996  xiv, 122 p. ; 23 cm
シリーズ名: Chicago lectures in mathematics
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目次情報: 続きを見る
Summary of Constructions
Foreword
Acknowledgments
Introduction
Definitions, examples and matrix groups / Ch. 1:
Clifford algebras / Ch. 2:
The Spin groups / Ch. 3:
Clifford modules and representations / Ch. 4:
Applications of Spin representations / Ch. 5:
The exceptional groups: construction of E[subscript 8] / Ch. 6:
Construction of a Lie group of type E[subscript 8] / Ch. 7:
The construction of Lie groups of type F[subscript 4], E[subscript 6], E[subscript 7] / Ch. 8:
The Dynkin diagrams of F[subscript 4], E[subscript 6], E[subscript 7], E[subscript 8] / Ch. 9:
The Weyl group of E[subscript 8] / Ch. 10:
Representations of E[subscript 6], E[subscript 7] / Ch. 11:
Direct construction of E[subscript 7] / Ch. 12:
Direct treatment of E[subscript 6] / Ch. 13:
Direct treatment of F[subscript 4], I / Ch. 14:
The Cayley numbers / Ch. 15:
Direct treatment of F[subscript 4], II: Jordan algebras / Ch. 16:
Appendix: Jordan algebras
References
Summary of Constructions
Foreword
Acknowledgments
28.

図書

図書
edited by Bent Ørsted, Henrik Schlichtkrull
出版情報: San Diego ; Tokyo : Academic Press, c1997  x, 343 p. ; 24 cm
シリーズ名: Perspectives in mathematics ; v. 17
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29.

図書

図書
Tammo tom Dieck
出版情報: Berlin : W. de Gruyter, 1987  x, 311 p. ; 25 cm
シリーズ名: De Gruyter studies in mathematics ; 8
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30.

図書

図書
David A. Vogan, Jr.
出版情報: Boston : Birkhaüser, 1981  xvii, 754 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 15
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31.

図書

図書
Adolf Karger, Josef Novák; translated by Michal Basch
出版情報: New York : Gordon and Breach Science Publishers, c1985  xv, 422 p. ; 24cm.
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32.

図書

図書
Andrew Pressley and Graeme Segal
出版情報: Oxford : Clarendon Press, 1986  viii, 318 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
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目次情報: 続きを見る
Introduction / 1:
Finite Dimensional Lie Groups / Part 1:
Groups of Smooth Maps / 3:
Central Extensions / 4:
The Root System: Kac-Moody Algebras / 5:
Loop Groups as Groups of Operators in Hilbert Space / 6:
The Grasmannian of Hilbert Space and the Determinant Time Bundle / 7:
The Fundamental Homogeneous Space / 8:
Representation Theory / Part 2:
The Fundamental Representation / 10:
The Borel-Weil Theory / 11:
The Spin Representation / 12:
'Blips' or 'Vertex-Operators' / 13:
The Kac Character Formula and the Bernstein-Gelfand-Gelfand Resolution / 14:
Introduction / 1:
Finite Dimensional Lie Groups / Part 1:
Groups of Smooth Maps / 3:
33.

図書

図書
Howard D. Fegan
出版情報: Singapore ; River Edge, N.J. : World Scientific, c1991  xiii, 131 p. ; 23 cm
シリーズ名: Series in pure mathematics ; v. 13
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34.

図書

図書
Jean-Pierre Serre
出版情報: Berlin ; Tokyo : Springer-Verlag, c1992  vii, 168 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1500
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目次情報: 続きを見る
Lie Algebras: Lie Algebras / Part I:
Definition and Examples
Filtered Groups and Lie Algebras
Universal Algebra of a Lie Algebra
Free Lie Algebras
Nilpotent and Solvable Lie Algebras
Semisimple Lie Algebras
Representations of sln
Complete Fields: Analytic Functions / Part II:
Analytic Manifolds
Analytic Groups
Lie Theory
Lie Algebras: Lie Algebras / Part I:
Definition and Examples
Filtered Groups and Lie Algebras
35.

図書

図書
A.N. Leznov, M.V. Saveliev ; translated from the Russian by D.A. Leites
出版情報: Basel ; Boston : Birkhäuser Verlag, 1992  xvii, 290 p. ; 24 cm
シリーズ名: Progress in physics ; v. 15
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36.

図書

図書
E.B. Vinberg, editor
出版情報: Providence, R.I. : American Mathematical Society, c1992  vii, 204 p. ; 26 cm
シリーズ名: Advances in Soviet mathematics ; v. 8
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目次情報: 続きを見る
Preface / A. L. Onishchik ; V. L. Popov ; E. B. Vinberg
$G$-manifolds with one-dimensional orbit space / A. V. Alekseevskii ; D. V. Alekseevskii
Arithmetic crystallographic groups generated by reflections and reflective hyperbolic lattices / V. O. Bugaenko
Invariant algebras / A. G. Elashvili
On the existence of Galois sections / L. Yu. Galitskii
On some cohomology invariants of compact homogeneous manifolds / V. V. Gorbatsevich
Explicit form of certain multivector invariants / A. A. Katanova
On the birational geometry of the space of ternary quartics / P. I. Katsylo
Rationality of the module variety of mathematical instantons with $c_2=5$
Holomorphic vector fields on super-Grassmannians / A. A. Serov
Affine quasihomogeneous normal $SL_2$-varieties: Hilbert function and blow-ups / D. I. Panyushev
Complexity of quasiaffine homogeneous varieties, $t$-decompositions, and affine homogeneous spaces of complexity $1$
On the "Lemma of Seshadri"
Coregular algebraic linear groups locally isomorphic to $SL_2$ / D. A. Shmelkin
An example of a nonarithmetic discrete group in the complex ball / O. V. Shvartsman
Free subsemigroups of the affine group, and the Schoenflies-Bieberbach theorem / G. A. Soifer
Preface / A. L. Onishchik ; V. L. Popov ; E. B. Vinberg
$G$-manifolds with one-dimensional orbit space / A. V. Alekseevskii ; D. V. Alekseevskii
Arithmetic crystallographic groups generated by reflections and reflective hyperbolic lattices / V. O. Bugaenko
37.

図書

図書
Derek W. Robinson
出版情報: Oxford : Clarendon Press, 1991  xi, 558 p. ; 24 cm
シリーズ名: Oxford mathematical monographs
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目次情報: 続きを見る
Introduction / 1:
Elliptic Operators / 2:
Analytic Elements / 3:
Semigroup Kernels / 4:
Second-Order Operators / 5:
Elliptic Operators with Variable Coefficients / 6:
Introduction / 1:
Elliptic Operators / 2:
Analytic Elements / 3:
38.

図書

図書
Mamoru Mimura, Hirosi Toda
出版情報: Providence, R.I. : American Mathematical Society, c1991  iv, 451 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 91
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目次情報: 続きを見る
Classical groups / Contents of Part I:
Covering spaces and fibre bundles
Cohomology groups of classical groups and their homogeneous spaces
The periodicity of $K\mathbf F$-groups and the homotopy groups
Compact Lie groups / Contents of Part II:
The Morse-Bott theory
Cohomology of exceptional groups
Classical groups / Contents of Part I:
Covering spaces and fibre bundles
Cohomology groups of classical groups and their homogeneous spaces
39.

図書

図書
William Fulton, Joe Harris
出版情報: New York ; Tokyo : Springer-Verlag, c1991  xv, 551 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 129 . Readings in mathematics
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目次情報: 続きを見る
Finite Groups / Part I:
Representations of Finite Groups / 1:
Characters / 2:
Examples; Induced Representations; Groups Algebras; Real Representations / 3:
Representations of Ed: Young Diagrams and Frobenius's Character Formula / 4:
Representation of Ud and GL2 and (Fq) / 5:
Weyl's Construction / 6:
Lie Groups and Lie Algebras / Part II:
Lie Groups / 7:
Lie Algebras and Lie Groups / 8:
Initial Classification of Lie Algebras / 9:
Lie Algebras in Dimensions One, Two, and Three / 10:
Representation of sI2 C / 11:
Representation of sI3 C, Part I / 12:
Representation of sI3 C, II: Mainly Lots of Examples / 13:
The Classical Lie Algebras and Their Representations / Part III:
The General Set-up: Analyzing the Structure and Representations of an Arbitrary Semi simple Lie Algebra / 14:
SI4 C and sIn C / 15:
Symplectic Lie Algebras / 16:
Sp6C and sp2n C / 17:
Orthogonal Lie Algebras / 18:
So6 C, so7 C, and som C / 19:
Spin Representations of so m C / 20:
Lie Theory / Part IV:
The Classification of Complex Simple Lie Algebras / 21:
G2 and Other Exceptional Lie Algebras / 22:
Complex Lie Groups; Characters / 23:
Weyl Character Formula / 24:
More Character Formulas / 25:
Real Lie Algebras and Lie Groups / 26:
Appendices A - F
Hints
Answers
References
Bibliography
Index of Symbols
Index
Finite Groups / Part I:
Representations of Finite Groups / 1:
Characters / 2:
40.

図書

図書
by N.Ja. Vilenkin and A.U. Klimyk ; translated from the Russian by V.A. Groza and A.A. Groza
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1993  xviii, 607 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series ; v. 74 . Representation of Lie groups and special functions / by N.Ja Vilenkin and A.U. Klimyk ; v. 2
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List of the Most Important Notations
Special Functions Connected with SO(n) and with Related Groups / 9:
Representations of Groups, Related to SO(n), in Non-Canonical Bases, Special Functions, and Integral Transforms / 10:
Special Functions Connected with the Groups U(n), U(n-1.1) and IU(n-1) / 11:
Representations of the Heisenberg Group and Special Functions / 12:
Representations of the Discrete Groups and Special Functions of Discrete Argument / 13:
Bibliography
Subject Index
List of the Most Important Notations
Special Functions Connected with SO(n) and with Related Groups / 9:
Representations of Groups, Related to SO(n), in Non-Canonical Bases, Special Functions, and Integral Transforms / 10:
41.

図書

図書
François Digne and Jean Michel
出版情報: Cambridge : Cambridge University Press, 1991  159 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 21
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目次情報: 続きを見る
Background results
Bruhat decomposition / 1:
Reduced subgroups of maximal rank, centralisers and semisimple elements / 2:
Rationality, Frobenius maps, Lang's theorem / 3:
Generalized induction associated with a bimodule / 4:
Mackey's theorem / 5:
Harish-Chandra theory / 6:
Complements on RGL
Duality of characters / 7:
Steinberg characters / 8:
l-adic cohomology
Deligne-Lusztig induction / 9:
Character formulae and their complements in Deligne-Lusztig induction / 10:
Geometric conjugation, Lusztig series / 11:
Background results
Bruhat decomposition / 1:
Reduced subgroups of maximal rank, centralisers and semisimple elements / 2:
42.

図書

図書
Mikio Ise, Masaru Takeuchi . Masaru Takeuchi
出版情報: Providence, R.I. : American Mathematical Society, c1991  iv, 259 p. ; 24 cm
シリーズ名: Translations of mathematical monographs ; v. 85
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Concept of Lie group, particularly, linear Lie group / Part I:
Compact Lie groups and semisimple
Lie groups Outline of the theory of Lie algebras
Riemannian manifolds / Part II:
Riemannian symmetric spaces
Riemannian symmetric spaces of semisimple type
Hermitian symmetric spaces
Concept of Lie group, particularly, linear Lie group / Part I:
Compact Lie groups and semisimple
Lie groups Outline of the theory of Lie algebras
43.

図書

図書
by N.Ja. Vilenkin and A.U. Klimyk
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1991  xxiii, 608 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series ; v. 72 . Representation of Lie groups and special functions ; v. 1
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44.

図書

図書
Zoltán Magyar
出版情報: Amsterdam ; New York : North-Holland, 1992  vii, 301 p. ; 25 cm
シリーズ名: North-Holland mathematics studies ; 168
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45.

図書

図書
by N.Ja. Vilenkin and A.U. Klimyk
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1992  xix, 629 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series ; v. 75 . Representation of Lie groups and special functions ; v. 3
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Series Editor's Preface
List of Special Symbols
Quantum Groups, q-Orthogonal Polynomials and Basic Hypergeometric Functions / 14:
Semisimple Lie Groups and Related Homogeneous Spaces / 15:
Representation of Semisimple Lie Groups and Their Matrix Elements / 16:
Group Representations and Special Functions of a Matrix Argument / 17:
Representations in the Gel'fand-Tsetlin Basis and Special Functions / 18:
Modular Forms, Theta Functions and Representations of Affine Lie Algebras / 19:
Bibliography
Notes
Subject Index
Series Editor's Preface
List of Special Symbols
Quantum Groups, q-Orthogonal Polynomials and Basic Hypergeometric Functions / 14:
46.

図書

図書
Victor Guillemin and Shlomo Sternberg
出版情報: Providence, R.I. : American Mathematical Society, c1990  vii, 88 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 42
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47.

図書

図書
[by] V.S. Varadarajan
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, [1974]  xiii, 430 p. ; 24 cm
シリーズ名: Prentice-Hall series in modern analysis
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48.

図書

図書
Joachim Hilgert, Karl Heinrich Hofmann and Jimmie D. Lawson
出版情報: Oxford : Clarendon Press , New York ; Tokyo : Oxford University Press, 1989  xxxviii, 645 p. ; 26 cm
シリーズ名: Oxford mathematical monographs
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The Geometry of Cones / 1:
Wedges in Lie Algebras / 2:
Invariant Cones / 3:
The Local Lie Theory of Semigroups / 4:
Subsemigroups of Lie Groups / 5:
Positivity / 6:
Embedding Semigroups into Lie Groups / 7:
The Geometry of Cones / 1:
Wedges in Lie Algebras / 2:
Invariant Cones / 3:
49.

図書

図書
by Frederic V. Bien
出版情報: Princeton, N.J. : Princeton University Press, 1990  131 p. ; 24 cm
シリーズ名: Mathematical notes ; 39
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50.

図書

図書
edited by William M. Boothby and Guido L. Weiss
出版情報: New York : M. Dekker, 1972  xiii, 487 p. ; 23 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 8
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