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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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Square integrable representations of classical p-adic groups corresponding to segments
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by Marko Tadić PDF
Represent. Theory 3 (1999), 58-89 Request permission

Abstract:

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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Additional Information
  • Marko Tadić
  • Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
  • ORCID: 0000-0002-6087-3765
  • Email: tadic@math.hr
  • 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: https://doi.org/10.1090/S1088-4165-99-00071-0
  • MathSciNet review: 1698200