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Character identities in the twisted endoscopy of real reductive groups

About this Title

Paul Mezo

Publication: Memoirs of the American Mathematical Society
Publication Year: 2013; Volume 222, Number 1042
ISBNs: 978-0-8218-7565-0 (print); 978-0-8218-9507-8 (online)
Published electronically: May 31, 2012
MSC: Primary 22E45, 11S37

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Table of Contents


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


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.

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