Exposing relative endoscopy in unitary symmetric spaces


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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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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Correspondence to Jason KC Polák.

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The author declares that he has no competing interests.

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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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  • Endoscopy
  • Orbital integral
  • Unitary group
  • Trace formula
  • Representation theory