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Representation Theory

ISSN 1088-4165



Propagation de paires couvrantes dans les groupes symplectiques

Author: Corinne Blondel
Journal: Represent. Theory 10 (2006), 399-434
MSC (2000): Primary 22E50; Secondary 20C08
Published electronically: October 3, 2006
MathSciNet review: 2266698
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Abstract: Let $ \pi$ be a self-dual supercuspidal representation of $ GL(N,F)$ and $ \rho$ a supercuspidal representation of $ Sp(2k,F)$, with $ F$ a local nonarchimedean field of odd residual characteristic. Given a type, indeed a $ Sp(2N+2k,F)$-cover, for the inertial class $ [GL(N,F) \times Sp(2k,F), \pi \otimes \rho ]_{Sp(2N+2k,F)}$ satisfying suitable hypotheses, we produce a type, indeed a $ Sp(2tN+2k,F)$-cover, for the inertial class $ [GL(N,F)^{\times t} \times Sp(2k,F), \pi^{\otimes t } \otimes \rho ]_{Sp(2tN+2k,F)}$, for any positive integer $ t$. We describe the corresponding Hecke algebra as a convolution algebra over an affine Weyl group of type $ \tilde C_t$ with quadratic relations inherited from the case $ t=1$ and the structural data for $ \pi$.

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Corinne Blondel
Affiliation: C.N.R.S. - Théorie des Groupes–Case 7012, Institut de Mathématiques de Jussieu, Université Paris 7, F-75251 PARIS Cedex 05.

Received by editor(s): September 28, 2005
Published electronically: October 3, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.