Exposing relative endoscopy in unitary symmetric spaces

  • Jason KC PolákEmail author
Open Access


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


Endoscopy 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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Copyright information

© Polák; licensee Springer. 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsMcGill UniversityMontrealCanada

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