UID:
almahu_9947367265702882
Format:
1 online resource (439 p.)
ISBN:
1-281-76767-0
,
9786611767679
,
0-08-087451-7
Series Statement:
Pure and applied mathematics ; 132
Content:
Real Productive Groups I
Note:
Description based upon print version of record.
,
Front Cover; Real Reductive Groups I; Copyright Page; Content; Preface; Introduction; Chapter 0. Background Material; Introduction; 0.1. Invariant measures on homogeneous spaces; 0.2. The structure of reductive Lie algebras; 0.3. The structure of compact Lie groups; 0.4. The universal enveloping algebra of a Lie algebra; 0.5. Some basic representation theory; 0.6. Modules over the universal enveloping algebra; Chapter 1. Elementary Representation Theory; Introduction; 1.1. General properties of representations; 1.2. Schur's lemma; 1.3. Square integrable representations
,
3.1. The Chevalley restriction theorem3.2. The Harish-Chandra isomorphism of the center of the universal enveloping algebra; 3.3. (g, K)-modules; 3.4. A basic theorem of Harish-Chandra; 3.5. The subquotient theorem; 3.6. The spherical principal series; 3.7. A Lemma of Osborne; 3.8. The subrepresentation theorem; 3.9. Notes and further results; 3.A. Appendices to Chapter 3; 3.A.1. Some associative algebra; 3.A.2. A Lemma of Harish-Chandra; Chapter 4. The Asymptotic Behavior of Matrix Coefficients; Introduction; 4.1. The Jacquet module of an admissible (g, K)-module
,
4.2. Three applications of the Jacquet module4.3. Asymptotic behavior of matrix coefficients; 4.4. Asymptotic expansions of matrix coefficients; 4.5. Harish-Chandra's Ξ-function; 4.6. Notes and further results; 4.A. Appendices to Chapter 4; 4.A.1. Asymptotic expansions; 4.A.2. Some inequalities; Chapter 5. The Langlands Classification; Introduction; 5.1. Tempered (g, K)-modules; 5.2. The principal series; 5.3. The intertwining integrals; 5.4. The Langlands classification; 5.5. Some applications of the classification; 5.6. SL(2, R); 5.7. SL(2, C); 5.8. Notes and further results
,
5.A. Appendices to Chapter 55.A.1. A Lemma of Langlands; 5.A.2. An a priori estimate; 5.A.3. Square integrability and the polar decomposition; Chapter 6. A Construction of the Fundamental Series; Introduction; 6.1. Relative Lie algebra cohomology; 6.2. A construction of ( f, K)-modules; 6.3. The Zuckerman functors; 6.4. Some vanishing theorems; 6.5. Blattner type formulas; 6.6. Irreducibility; 6.7. Unitarizability; 6.8. Temperedness and square integrability; 6.9. The case of disconnected G; 6.10. Notes and further results; 6.A. Appendices to Chapter 6; 6.A.1. Some homological algebra
,
6.A.2. Partition functions
,
English
Additional Edition:
ISBN 0-12-732960-9
Language:
English
