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
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Borovoi M: Abelian Galois Cohomology of Reductive Groups vol. 626. American Mathematical Society, 201 Charles Street, Providence, RI. USA 02904-2294 (1998).
Getz, JR, Wambach, E: Twisted relative trace formulae with a view towards unitary groups. Amer. J. Math. 135, 1–57 (2013).
Kottwitz, R: Transfer factors for lie algebras. Representation Theory Am. Math. Soc. 3(6), 127–138 (1999).
Levy, P: Involutions of reductive lie algebras in positive characteristic. Adv. Mathematics. 210(2), 505–559 (2007).
Ngô, BC: Le lemme fondamental pour les algebres de lie. Publications mathématiques de l’IHÉS. 111(1), 1–169 (2010).
Acknowledgements
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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Polák, J.K. Exposing relative endoscopy in unitary symmetric spaces. Mathematical Sciences 2, 9 (2015). https://doi.org/10.1186/s40687-015-0024-y
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DOI: https://doi.org/10.1186/s40687-015-0024-y