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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Types in reductive $p$-adic groups: The Hecke algebra of a cover


Authors: Colin J. Bushnell and Philip C. Kutzko
Journal: Proc. Amer. Math. Soc. 129 (2001), 601-607
MSC (1991): Primary 22E50, 22D99
Published electronically: August 29, 2000
MathSciNet review: 1712937
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Abstract: In this paper, $F$ is a non-Archimedean local field and $G$ is the group of $F$-points of a connected reductive algebraic group defined over $F$. Also, $\tau $ is an irreducible representation of a compact open subgroup $J$ of $G$, the pair $(J,\tau )$ being a type in $G$. The pair $(J,\tau )$ is assumed to be a cover of a type $(J_{L},\tau _{L})$ in a Levi subgroup $L$ of $G$. We give conditions, generalizing those of earlier work, under which the Hecke algebra $\mathcal H(G,\tau )$ is the tensor product of a canonical image of $\mathcal H(L,\tau _{L})$ and a sub-algebra $\mathcal H(K,\tau )$, for a compact open subgroup $K$ of $G$ containing $J$.


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Additional Information

Colin J. Bushnell
Affiliation: Department of Mathematics, King’s College, Strand, London WC2R 2LS, United Kingdom
Email: bushnell@mth.kcl.ac.uk

Philip C. Kutzko
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: pkutzko@blue.weeg.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05665-3
PII: S 0002-9939(00)05665-3
Keywords: $p$-adic reductive group, type, cover, Hecke algebra
Received by editor(s): April 28, 1999
Published electronically: August 29, 2000
Additional Notes: The research of the second-named author was partially supported by NSF grant DMS-9003213
Communicated by: Rebecca A. Herb
Article copyright: © Copyright 2000 American Mathematical Society