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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Typical representations via fixed point sets in Bruhat–Tits buildings
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by Peter Latham and Monica Nevins PDF
Represent. Theory 25 (2021), 1021-1048 Request permission

Abstract:

For a tame supercuspidal representation $\pi$ of a connected reductive $p$-adic group $G$, we establish two distinct and complementary sufficient conditions, formulated in terms of the geometry of the Bruhat–Tits building of $G$, for the irreducible components of its restriction to a maximal compact subgroup to occur in a representation of $G$ which is not inertially equivalent to $\pi$. The consequence is a set of broadly applicable tools for addressing the branching rules of $\pi$ and the unicity of $[G,\pi ]_G$-types.
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Additional Information
  • Peter Latham
  • Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
  • MR Author ID: 1145038
  • Email: platham@uottawa.ca
  • Monica Nevins
  • Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada
  • MR Author ID: 649935
  • ORCID: 0000-0003-1948-3914
  • Email: mnevins@uottawa.ca
  • Received by editor(s): May 13, 2021
  • Received by editor(s) in revised form: September 2, 2021
  • Published electronically: December 16, 2021
  • Additional Notes: The first author’s research was supported by the Heilbronn Institute for Mathematical Research. The second author’s research was supported by a Discovery Grant from NSERC Canada
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 1021-1048
  • MSC (2020): Primary 22E50
  • DOI: https://doi.org/10.1090/ert/590
  • MathSciNet review: 4353893