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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.

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Square integrable representations of classical p-adic groups corresponding to segments
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by Marko Tadić
Represent. Theory 3 (1999), 58-89
Published electronically: June 9, 1999


Let $S_n$ be either the group $Sp(n)$ or $SO(2n+1)$ over a $p$-adic field $F$. Then Levi factors of maximal parabolic subgroups are (isomorphic to) direct products of $GL(k)$ and $S_{n-k}$, with $1\leq k\leq n$. The square integrable representations which we define and study in this paper (and prove their square integrability), are subquotients of reducible representations Ind$_P^{S_n}(\delta \otimes \sigma ),$ where $\delta$ is an essentially square integrable representation of $GL(k)$, and $\sigma$ is a cuspidal representation of $S_{n-k}$. These square integrable representations play an important role in a construction of more general square integrable representations.
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Bibliographic Information
  • Marko Tadić
  • Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
  • ORCID: 0000-0002-6087-3765
  • Email:
  • Received by editor(s): July 17, 1998
  • Received by editor(s) in revised form: December 6, 1998
  • Published electronically: June 9, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 58-89
  • MSC (1991): Primary 22E50
  • DOI:
  • MathSciNet review: 1698200