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TEMPERED SPECTRAL TRANSFER IN THE TWISTED ENDOSCOPY OF REAL GROUPS

Part of: Lie groups Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  17 December 2014

Paul Mezo
Paul Mezo*
Affiliation:
The School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada ([email protected])
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Abstract

Suppose that $G$ is a connected reductive algebraic group defined over $\mathbf{R}$, $G(\mathbf{R})$ is its group of real points, ${\it\theta}$ is an automorphism of $G$, and ${\it\omega}$ is a quasicharacter of $G(\mathbf{R})$. Kottwitz and Shelstad defined endoscopic data associated to $(G,{\it\theta},{\it\omega})$, and conjectured a matching of orbital integrals between functions on $G(\mathbf{R})$ and its endoscopic groups. This matching has been proved by Shelstad, and it yields a dual map on stable distributions. We express the values of this dual map on stable tempered characters as a linear combination of twisted characters, under some additional hypotheses on $G$ and ${\it\theta}$.

Keywords

twisted endoscopyspectral transfer

MSC classification

Primary: 22E45: Representations of Lie and linear algebraic groups over real fields
Secondary: 22E47: Representations of Lie and real algebraic groups 11S37: Langlands-Weil conjectures, nonabelian class field theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 3 , July 2016 , pp. 569 - 612
Copyright
© Cambridge University Press 2014 

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