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Character Identities in the Twisted Endoscopy of Real Reductive Groups
Paul Mezo, Carleton University, Ottawa, ON, Canada

Memoirs of the American Mathematical Society
2013; 94 pp; softcover
Volume: 222
ISBN-10: 0-8218-7565-5
ISBN-13: 978-0-8218-7565-0
List Price: US$69
Individual Members: US$41.40
Institutional Members: US$55.20
Order Code: MEMO/222/1042
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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

  • Introduction
  • Notation
  • The foundations of real twisted endoscopy
  • The Local Langlands Correspondence
  • Tempered essentially square-integrable representations
  • Spectral transfer for essentially square-integrable representations
  • Spectral transfer for limits of discrete series
  • Appendix A. Parabolic descent for geometric transfer factors
  • Bibliography
  • Index
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