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
- 1.Borovoi M: Abelian Galois Cohomology of Reductive Groups vol. 626. American Mathematical Society, 201 Charles Street, Providence, RI. USA 02904-2294 (1998).Google Scholar
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