Preface to the Princeton Landmarks in Mathematics Edition |
Preface |
Acknowledgments |
Scope of the Theory / Chapter I.: |
The Classical Groups / 1.: |
Cartan Decomposition / 2.: |
Representations / 3.: |
Concrete Problems in Representation Theory / 4.: |
Abstract Theory for Compact Groups / 5.: |
Application of the Abstract Theory to Lie Groups / 6.: |
Problems / 7.: |
Representations of SU(2), SL(2, R), and SL(2, C) / Chapter II.: |
The Unitary Trick |
Irreducible Finite-Dimensional Complex-Linear Representations of sl(2, C) |
Finite-Dimensional Representations of sl(2, C) |
Irreducible Unitary Representations of SL(2, C) |
Irreducible Unitary Representations of SL(2, R) |
Use of SU(1, 1) |
Plancherel Formula |
C[superscript [infinity] Vectors and the Universal Enveloping Algebra / 8.: |
Universal Enveloping Algebra |
Actions on Universal Enveloping Algebra |
C[superscript [infinity] Vectors |
Garding Subspace |
Representations of Compact Lie Groups / Chapter IV.: |
Examples of Root Space Decompositions |
Roots |
Abstract Root Systems and Positivity |
Weyl Group, Algebraically |
Weights and Integral Forms |
Centalizers of Tori |
Theorem of the Highest Weight |
Verma Modules |
Weyl Group, Analytically / 9.: |
Weyl Character Formula / 10.: |
Structure Theory for Noncompact Groups / 11.: |
Cartan Decomposition and the Unitary Trick |
Iwasawa Decomposition |
Regular Elements, Weyl Chambers, and the Weyl Group |
Other Decompositions |
Parabolic Subgroups |
Integral Formulas |
Borel-Weil Theorem |
Holomorphic Discrete Series / Chapter VI.: |
Holomorphic Discrete Series for SU(1, 1) |
Classical Bounded Symmetric Domains |
Harish-Chandra Decomposition |
Finiteness of an Integral |
Induced Representations / Chapter VII.: |
Three Pictures |
Elementary Properties |
Bruhat Theory |
Formal Intertwining Operators |
Gindikin-Karpelevic Formula |
Estimates on Intertwining Operators, Part I |
Analytic Continuation of Intertwining Operators, Part I |
Spherical Functions |
Finite-Dimensional Representations and the H function |
Estimates on Intertwining Operators, Part II |
Tempered Representations and Langlands Quotients |
Admissible Representations / 12.: |
Motivation |
Invariant Subspaces |
Framework for Studying Matrix Coefficients |
Harish-Chandra Homomorphism |
Infinitesimal Character |
Differential Equations Satisfied by Matrix Coefficients |
Asymptotic Expansions and Leading Exponents |
First Application: Subrepresentation Theorem |
Second Application: Analytic Continuation of Interwining Operators, Part II |
Third Application: Control of K-Finite Z(g[superscript C])-Finite Functions |
Asymptotic Expansions near the Walls |
Fourth Application: Asymptotic Size of Matrix Coefficients / 13.: |
Fifth Application: Identification of Irreducible Tempered Representations / 14.: |
Sixth Application: Langlands Classification of Irreducible Admissible Representations / 15.: |
Construction of Discrete Series / 16.: |
Infinitesimally Unitary Representations |
A Third Way of Treating Admissible Representations |
Equivalent Definitions of Discrete Series |
Motivation in General and the Construction in SU(1, 1) |
Finite-Dimensional Spherical Representations |
Duality in the General Case |
Limitations on K Types |
Lemma on Linear Independence |
Global Characters / Chapter X.: |
Existence |
Character Formulas for SL(2, R) |
Induced Characters |
Differential Equations |
Analyticity on the Regular Set, Overview and Example |
Analyticity on the Regular Set, General Case |
Formula on the Regular Set |
Behavior on the Singular Set |
Families of Admissible Representations |
Introduction to Plancherel Formula / Chapter XI.: |
Constructive Proof for SU(2) |
Constructive Proof for SL(2, C) |
Constructive Proof for SL(2, R) |
Ingredients of Proof for General Case |
Scheme of Proof for General Case |
Properties of F[subscript f] |
Hirai's Patching Conditions |
Exhaustion of Discrete Series / Chapter XII.: |
Boundedness of Numerators of Characters |
Use of Patching Conditions |
Formula for Discrete Series Characters |
Schwartz Space |
Tempered Distributions |
Limits of Discrete Series |
Discrete Series of M |
Schmid's Identity |
Ideas and Ingredients / Chapter XIII.: |
Real-Rank-One Groups |
Real-Rank-One Groups, Part II |
Averaged Discrete Series |
Sp (2, R) |
General Case |
Irreducible Tempered Representations / Chapter XIV.: |
SL(2, R) from a More General Point of View |
Eisenstein Integrals |
Asymptotics of Eisenstein Integrals |
The [eta] Functions for Intertwining Operators |
First Irreducibility Results |
Normalization of Intertwining Operators and Reducibility |
Connection with Plancherel Formula when dim A = 1 |
Harish-Chandra's Completeness Theorem |
R Group |
Action by Weyl Group on Representations of M |
Multiplicity One Theorem |
Zuckerman Tensoring of Induced Representations |
Generalized Schmid Identities |
Inversion of Generalized Schmid Identities |
Complete Reduction of Induced Representations |
Classification |
Revised Langlands Classification / 17.: |
Minimal K Types / 18.: |
Definition and Formula |
Inversion Problem |
Connection with Intertwining Operators |
Unitary Representations / Chapter XVI.: |
SL(2, R) and SL(2, C) |
Continuity Arguments and Complementary Series |
Criterion for Unitary Representations |
Reduction to Real Infinitesimal Character |
Elementary Theory of Lie Groups / Appendix A: |
Lie Algebras |
Structure Theory of Lie Algebras |
Fundamental Group and Covering Spaces |
Topological Groups |
Vector Fields and Submanifolds |
Lie Groups |
Regular Singular Points of Partial Differential Equations / Appendix B: |
Summary of Classical One-Variable Theory |
Uniqueness and Analytic Continuation of Solutions in Several Variables |
Analog of Fundamental Matrix |
Regular Singularities |
Systems of Higher Order |
Leading Exponents and the Analog of the Indicial Equation |
Uniqueness of Representation |
Roots and Restricted Roots for Classical Groups / Appendix C: |
Complex Groups |
Noncompact Real Groups |
Roots vs. Restricted Roots in Noncompact Real Groups |
Notes |
References |
Index of Notation |
Index |
Preface to the Princeton Landmarks in Mathematics Edition |
Preface |
Acknowledgments |