**Memoirs of the American Mathematical Society**

2013;
94 pp;
Softcover

MSC: Primary 22; 11;

Print ISBN: 978-0-8218-7565-0

Product Code: MEMO/222/1042

List Price: $69.00

Individual Member Price: $41.40

**Electronic ISBN: 978-0-8218-9507-8
Product Code: MEMO/222/1042.E**

List Price: $69.00

Individual Member Price: $41.40

# Character Identities in the Twisted Endoscopy of Real Reductive Groups

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*Paul Mezo*

Suppose \(G\) is a real reductive algebraic group, \(\theta\) is an automorphism of \(G\), and \(\omega\) is a quasicharacter of the group of real points \(G(\mathbf{R})\). Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups \(H\). The Local Langlands Correspondence partitions the admissible representations of \(H(\mathbf{R})\) and \(G(\mathbf{R})\) into \(L\)-packets. The author proves twisted character identities between \(L\)-packets of \(H(\mathbf{R})\) and \(G(\mathbf{R})\) comprised of essential discrete series or limits of discrete series.

#### Table of Contents

# Table of Contents

## Character Identities in the Twisted Endoscopy of Real Reductive Groups

- Chapter 1. Introduction 18 free
- Chapter 2. Notation 714 free
- Chapter 3. The foundations of real twisted endoscopy 916
- Chapter 4. The Local Langlands Correspondence 1522
- Chapter 5. Tempered essentially square-integrable representations 1926
- Chapter 6. Spectral transfer for essentially square-integrable representations 3340
- Chapter 7. Spectral transfer for limits of discrete series 7380
- Appendix A. Parabolic descent for geometric transfer factors 8794
- Bibliography 8996
- Index 93100 free