Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Gold Open Access
Representation Theory
Representation Theory
ISSN 1088-4165


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

Author: Alexandru Tupan
Journal: Represent. Theory 10 (2006), 158-163
MSC (2000): Primary 20G05
Published electronically: March 14, 2006
MathSciNet review: 2219111
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. I. N. Bernšteĭn and A. V. Zelevinskiĭ, Representations of the group 𝐺𝐿(𝑛,𝐹), where 𝐹 is a local non-Archimedean field, Uspehi Mat. Nauk 31 (1976), no. 3(189), 5–70 (Russian). MR 0425030 (54 #12988)
  • 2. Daniel Bump, Automorphic forms and representations, Cambridge Studies in Advanced Mathematics, vol. 55, Cambridge University Press, Cambridge, 1997. MR 1431508 (97k:11080)
  • 3. Schémas en groupes. I: Propriétés générales des schémas en groupes, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 151, Springer-Verlag, Berlin-New York, 1970 (French). MR 0274458 (43 #223a)
  • 4. I. M. Gel′fand and D. A. Každan, Representations of the group 𝐺𝐿(𝑛,𝐾) where 𝐾 is a local field, Funkcional. Anal. i Priložen. 6 (1972), no. 4, 73–74 (Russian). MR 0333080 (48 #11405)
    I. M. Gel′fand and D. A. Kajdan, Representations of the group 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, pp. 95–118. MR 0404534 (53 #8334)
  • 5. Maxwell Rosenlicht, A remark on quotient spaces, An. Acad. Brasil. Ci. 35 (1963), 487–489. MR 0171782 (30 #2009)

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 20G05

Retrieve articles in all journals with MSC (2000): 20G05

Additional Information

Alexandru Tupan
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia