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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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On typical representations for depth-zero components of split classical groups
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by Santosh Nadimpalli and Amiya Kumar Mondal PDF
Represent. Theory 23 (2019), 249-277 Request permission

Abstract:

Let $\mathbf {G}$ be a split classical group over a non-Archimedean local field $F$ with the cardinality of the residue field $q_F>5$. Let $M$ be the group of $F$-points of a Levi factor of a proper $F$-parabolic subgroup of $\mathbf {G}$. Let $[M, \sigma _M]_M$ be an inertial class such that $\sigma _M$ contains a depth-zero Moy–Prasad type of the form $(K_M, \tau _M)$, where $K_M$ is a hyperspecial maximal compact subgroup of $M$. Let $K$ be a hyperspecial maximal compact subgroup of $\mathbf {G}(F)$ such that $K$ contains $K_M$. In this article, we classify $\mathfrak {s}$-typical representations of $K$. In particular, we show that the $\mathfrak {s}$-typical representations of $K$ are precisely the irreducible subrepresentations of $\operatorname {ind}_J^K\lambda$, where $(J, \lambda )$ is a level-zero $G$-cover of $(K\cap M, \tau _M)$.
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Additional Information
  • Santosh Nadimpalli
  • Affiliation: IMAPP, Radboud Universiteit Nijmegen, Heyendaalseweg 135, 6525AJ Nijmegen, the Netherlands
  • MR Author ID: 1183126
  • ORCID: 0000-0002-2637-6159
  • Email: nvrnsantosh@gmail.com, santosh.nadimpalli@.ru.nl
  • Amiya Kumar Mondal
  • Affiliation: Department of Mathematics, Bar-Ilan University, Ramat Gan 529002, Israel
  • MR Author ID: 1115151
  • Email: amiya96@gmail.com, amiya@math.biu.ac.il
  • Received by editor(s): October 2, 2018
  • Received by editor(s) in revised form: August 7, 2019
  • Published electronically: September 12, 2019
  • Additional Notes: The first author was supported by the NWO Vidi grant “A Hecke algebra approach to the local Langlands correspondence” (nr. 639.032.528)
    The second author was funded by Israel Science Foundation grant No. 421/17 (Mondal)
  • © Copyright 2019 American Mathematical Society
  • Journal: Represent. Theory 23 (2019), 249-277
  • MSC (2010): Primary 22E50; Secondary 11F70
  • DOI: https://doi.org/10.1090/ert/532
  • MathSciNet review: 4007167