**Contemporary Mathematics**

Volume: 472;
2008;
246 pp;
Softcover

MSC: Primary 22; 20;

Print ISBN: 978-0-8218-4366-6

Product Code: CONM/472

List Price: $86.00

Individual Member Price: $68.80

**Electronic ISBN: 978-0-8218-8151-4
Product Code: CONM/472.E**

List Price: $86.00

Individual Member Price: $68.80

# Representation Theory of Real Reductive Lie Groups

Share this page *Edited by *
*James Arthur; Wilfried Schmid; Peter E. Trapa*

The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference “Representation Theory of Real Reductive Lie Groups” held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature.

This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields.

#### Table of Contents

# Table of Contents

## Representation Theory of Real Reductive Lie Groups

- Contents v6 free
- Preface vii8 free
- Guide to the Atlas Software: Computational Representation Theory of Real Reductive Groups 110 free
- Problems for Real Groups 3948
- 1. Endoscopic transfer 3948
- 2. Endoscopic character identities 4251
- 3. Orthogonality relations 4453
- 4. Weighted orbital integrals 4655
- 5. Intertwining operators and residues 4756
- 6. Twisted groups 4958
- 7. Trace identities for intertwining operators 5261
- 8. Construction of A-packets 5463
- 9. Properties of A-packets 5766
- 10. Functorial transfer 5867
- References 6069

- Unitarizable Minimal Principal Series of Reductive Groups 6372
- Computations in Real Tori 137146
- Weighted Orbital Integrals 153162
- Introduction to Endoscopy 175184
- 1. Introduction 176185
- 2. Some basic definitions 177186
- 3. GL(2) 181190
- 4. SL(2) 183192
- 5. U(2, 1) 189198
- 6. Galois cohomology and Endoscopy 193202
- 6.1. Non abelian hypercohomology 193202
- 6.2. Galois cohomology and abelianized cohomology 195204
- 6.3. Stable conjugacy and k-orbital integrals 197206
- 6.4. Stable conjugacy and compact Cartan subgroups over R 200209
- 6.5. Endoscopic groups 201210
- 6.6. The dual picture 202211
- 6.7. Endoscopic transfer 204213

- 7. Discrete series and endoscopy 206215
- 8. Further developments 209218
- 9. Bibliography 212221

- Tempered Endoscopy for Real Groups I: Geometric Transfer with Canonical Factors 215224

#### Readership

Graduate students and research mathematicians interested in representations in Lie groups.