Exposing relative endoscopy in unitary symmetric spaces

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Abstract

We introduce a new class of symmetric space orbital integrals important for applications in certain relative trace formula appearing in the theory of automorphic representations. We verify a fundamental lemma for U2×U2↪U4 via an explicit calculation, giving the first known example of endoscopy for symmetric spaces and showing strong evidence that there is a general theory of endoscopy lurking in this situation.

AMS subject classification Primary 20G05

Keywords

Endoscopy Orbital integral Unitary group Trace formula Representation theory 

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Copyright information

© Polák; licensee Springer. 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.

Authors and Affiliations

  1. 1.Department of MathematicsMcGill UniversityMontrealCanada

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