Exposing relative endoscopy in unitary symmetric spaces
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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
KeywordsEndoscopy Orbital integral Unitary group Trace formula Representation theory
The author would like to thank Jayce R. Getz for suggesting this problem, for a thorough reading of the manuscript and for encouragement. The author also thanks the anonymous referee for suggesting some improvements to the exposition and pointing out a typographical error.
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