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

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.

• 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