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Square integrable representations of classical $p$-adic groups corresponding to segments


Author: Marko Tadic
Journal: Represent. Theory 3 (1999), 58-89
MSC (1991): Primary 22E50
DOI: https://doi.org/10.1090/S1088-4165-99-00071-0
Published electronically: June 9, 1999
MathSciNet review: 1698200
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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 Tadic
Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Email: tadic@math.hr

DOI: https://doi.org/10.1090/S1088-4165-99-00071-0
Received by editor(s): July 17, 1998
Received by editor(s) in revised form: December 6, 1998
Published electronically: June 9, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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