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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 the socles of certain parabolically induced representations of $p$-adic classical groups
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by Hiraku Atobe PDF
Represent. Theory 26 (2022), 515-541 Request permission


In this paper, we consider representations of $p$-adic classical groups parabolically induced from the products of shifted Speh representations and unitary representations of Arthur type of good parity. We describe how to compute the socles (the maximal semisimple subrepresentations) of these representations. As a consequence, we can determine whether these representations are reducible or not. In particular, our results produce many unitary representations, which appear in the complementary series.
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Additional Information
  • Hiraku Atobe
  • Affiliation: Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810, Japan
  • MR Author ID: 1105443
  • Email:
  • Received by editor(s): September 28, 2021
  • Received by editor(s) in revised form: February 20, 2022
  • Published electronically: April 25, 2022
  • Additional Notes: The author was supported by JSPS KAKENHI Grant Number 19K14494.
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 515-541
  • MSC (2020): Primary 22E50; Secondary 22D10
  • DOI:
  • MathSciNet review: 4412277