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1.

図書

図書
Susumu Ariki
出版情報: Providence, R.I. : American Mathematical Society, c2002  vii, 158 p. ; 26 cm
シリーズ名: University lecture series ; 26
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Introduction
The Serre relations Kac-Moody Lie algebras
Crystal bases of $U_v$-modules
The tensor product of crystals
Crystal bases of $U_v^-$
The canonical basis
Existence and uniqueness (part I)
Existence and uniqueness (part II)
The Hayashi realization Description of the crystal graph of $V(\Lambda)$
An overview of the application to Hecke algebras
The Hecke algebra of type $G(m,1,n)$
The proof of Theorem 12.5
Reference guide
Bibliography
Index
Introduction
The Serre relations Kac-Moody Lie algebras
Crystal bases of $U_v$-modules
2.

図書

図書
Jin Hong, Seok-Jin Kang
出版情報: Providence, R.I. : American Mathematical Society, c2002  xviii, 307 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 42
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Lie algebras and Hopf algebras
Kac-Moody algebras Quantum groups
Crystal bases Existence and uniqueness of crystal bases
Global bases Young tableaux and crystals
Crystal graphs for classical Lie algebras
Solvable lattice models Perfect crystals
Combinatorics of Young walls
Bibliography
Index of symbols
Index
Lie algebras and Hopf algebras
Kac-Moody algebras Quantum groups
Crystal bases Existence and uniqueness of crystal bases
3.

図書

図書
Gilles Pisier
出版情報: Berlin ; Tokyo : Springer-Verlag, c2001  vi, 198 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1618
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4.

図書

図書
Bruce E. Sagan
出版情報: New York : Springer, c2001  xv, 238 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 203
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Group Representations
Representations of the Symmetric Group
Combinatorial Algorithms
Symmetric Functions
Applications and Generalizations
Group Representations
Representations of the Symmetric Group
Combinatorial Algorithms
5.

図書

図書
Alexander Kleshchev
出版情報: Cambridge : Cambridge University Press, c2005  xiv, 277 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 163
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Preface
Linear Representations / Part I:
Notations and generalities / 1:
Symmetric groups I / 2:
Degenerate affine Hecke algebra / 3:
First results on Hn-modules / 4:
Crystal operators / 5:
Character calculations / 6:
Integral representations and cyclotomic Hecke algebras / 7:
Functors ei? and fi? / 8:
Construction of UZ+ and irreducible modules / 9:
Identification of the crystal / 10:
Symmetric groups II / 11:
Projective Representations / Part II:
Generalities on superalgebra / 12:
Sergeev superalgebras / 13:
Affine Sergeev superalgebras / 14:
Integral representations and cyclotomic Sergeev algebras / 15:
First results on Xn-modules / 16:
Crystal operators for Xn / 17:
Character calculations for Xn / 18:
Operators ei? and fi? / 19:
Double covers / 20:
References
Index
Preface
Linear Representations / Part I:
Notations and generalities / 1:
6.

図書

図書
G. Lusztig
出版情報: Providence, R.I. : American Mathematical Society, c2003  vi, 136 p. ; 26 cm
シリーズ名: CRM monograph series ; v. 18
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7.

図書

図書
Michel Brion, Shrawan Kumar
出版情報: Boston : Birkhäuser, c2005  viii, 250 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 231
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8.

図書

図書
George W. Mackey
出版情報: New York : W.A. Benjamin , Torino : Editore Boringhieri, 1968  viii, 167 p. ; 23 cm
シリーズ名: Pubblicazioni della Classe di scienze / Scuola Normale Superiore
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9.

図書

図書
G.I. Olshanski, editor
出版情報: Providence, R.I. : American Mathematical Society, c1998  xiii, 271 p. ; 27 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 181 . Advances in the mathematical sciences (formerly Advances in Soviet mathematics) ; 35
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Screenings and a universal Lie-de Rham cocycle / V. Ginzburg ; V. Schechtman
Interlacing measures / S. Kerov
Quasicommuting families of quantum Plucker coordinates / B. Leclerc ; A. Zelevinsky
Factorial supersymmetric Schur functions and super Capelli identities / A. Molev Yangians ; Capelli identities ; M. L. Nazarov
Hinges and the Study-Semple-Satake-Furstenberg-De Concini-Procesi-Oshima boundary / Y. Neretin
Multiplicities and Newton polytopes / A. Okounkov
Shifted Schur functions II. The binomial formula for characters of classical groups and its applications / G. Olshanski
Screenings and a universal Lie-de Rham cocycle / V. Ginzburg ; V. Schechtman
Interlacing measures / S. Kerov
Quasicommuting families of quantum Plucker coordinates / B. Leclerc ; A. Zelevinsky
10.

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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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.:
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