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

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On representations of elementary subgroups of Chevalley groups over algebras


Author: Yu Chen
Journal: Proc. Amer. Math. Soc. 123 (1995), 2357-2361
MSC: Primary 20G35; Secondary 20G05
MathSciNet review: 1283542
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that every nontrivial linear or projective representation of the elementary subgroup of a Chevalley group over an algebra containing an infinite field must have degree greater than or equal to the square root of the dimension of the corresponding Chevalley-Demazure group scheme adding 1 and the equality emerges only if the Chevalley group is of type $ {A_n}$ for $ n \geq 1$.


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

  • [1] Eiichi Abe, Chevalley groups over local rings, Tôhoku Math. J. (2) 21 (1969), 474–494. MR 0258837 (41 #3483)
  • [2] Armand Borel, Properties and linear representations of Chevalley groups, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 1–55. MR 0258838 (41 #3484)
  • [3] Yu Chen, Isomorphic Chevalley groups over integral domains, Rend. Sem. Mat. Univ. Padova 92 (1994), 231–237. MR 1320490 (96d:20041)
  • [4] C. Chevalley, Certains schémas de groupes semisimples, Sém. Bourbaki Exp. 219 (1960/61).
  • [5] 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)
  • [6] Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335 (57 #6215)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20G35, 20G05

Retrieve articles in all journals with MSC: 20G35, 20G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1283542-7
PII: S 0002-9939(1995)1283542-7
Keywords: Chevalley group, elementary subgroup, algebra, representation
Article copyright: © Copyright 1995 American Mathematical Society