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A triangulation of $ \mathrm{GL}(n,F)$

Author(s): Alexandru Tupan
Journal: Represent. Theory 10 (2006), 158-163.
MSC (2000): Primary 20G05
Posted: March 14, 2006
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Abstract: Let $ F$ be a non-Archimedian field. We prove that each open and compact subset of $ \mathrm{GL}_n(F)$ can be decomposed into finitely many open, compact, and self-conjugate subsets. As a corollary, we obtain a short, elementary proof of a well-known theorem of I.M. Gelfand and D.A. Kazhdan.

References:

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Bernstein, I.N. and Zelevinsky, A.N. Representations of the group $ \mathrm{GL}(n,F)$ where $ F$ is a local non-Archimedian field, Russian Mathematical Surveys 3 (1976), 1-68. MR 0425030 (54:12988)

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Bump, D. Automorphic forms and representations, Cambridge Studies in Advanced Mathematics, 55, Cambridge University Press, Cambridge, 1997. MR 1431508 (97k:11080)

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Demazure, M. and Grothendieck, A. Schémas en groupes I. Propriétés générales des schémas en groupes. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3), Springer Lecture Notes, Vol. 151, 1970. MR 0274458 (43:223a)

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Gelfand, I.M. and Kazhdan, D.A. (1) Representations of the group $ \mathrm{GL}(n,K)$ where $ K$ is a local field, Funkcional Anal. i Prilozen 6 (1972), no 4, 73-74; (2) Representations of the group $ \mathrm{GL}(n,K)$ where $ K$ is a local field, Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest 1971), Halsted, New York (1975), 95-118. MR 0333080 (48:11405); MR 0404534 (53:8334)

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Rosenlicht, M., A remark on quotient spaces, An. Acad. Brasil, 35 (1963), 487-489. MR 0171782 (30:2009)

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Additional Information:

Alexandru Tupan
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: tupan@math.msu.edu

DOI: 10.1090/S1088-4165-06-00224-X
PII: S 1088-4165(06)00224-X
Received by editor(s): December 17, 2003
Received by editor(s) in revised form: February 18, 2006
Posted: March 14, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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