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# memo_has_moved_text(); Character identities in the twisted endoscopy of real reductive groups

Paul Mezo

Publication: Memoirs of the American Mathematical Society
Publication Year 2012: Volume 222, Number 1042
ISBNs: 978-0-8218-7565-0 (print); 978-0-8218-9507-8 (online)
DOI: http://dx.doi.org/10.1090/S0065-9266-2012-00661-7
Published electronically: May 31, 2012
MSC (2010): Primary 22E45, 11S37

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Chapters

• Chapter 1. Introduction
• Chapter 2. Notation
• Chapter 3. The foundations of real twisted endoscopy
• Chapter 4. The local Langlands correspondence
• Chapter 5. Tempered essentially square-integrable representations
• Chapter 6. Spectral transfer for essentially square-integrable representations
• Chapter 7. Spectral transfer for limits of discrete series
• Appendix A. Parabolic descent for geometric transfer factors

### Abstract

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. We prove twisted character identities between $L$-packets of $H(\mathbf {R})$ and $G(\mathbf {R})$ comprised of essential discrete series or limits of discrete series.