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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the socles of certain parabolically induced representations of $p$-adic classical groups
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by Hiraku Atobe
Represent. Theory 26 (2022), 515-541
Published electronically: April 25, 2022


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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Bibliographic 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