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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On representations of elementary subgroups of Chevalley groups over algebras
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by Yu Chen
Proc. Amer. Math. Soc. 123 (1995), 2357-2361
DOI: https://doi.org/10.1090/S0002-9939-1995-1283542-7

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
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  • Yu Chen, Isomorphic Chevalley groups over integral domains, Rend. Sem. Mat. Univ. Padova 92 (1994), 231–237. MR 1320490
  • C. Chevalley, Certains schémas de groupes semisimples, Sém. Bourbaki Exp. 219 (1960/61).
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  • Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 2357-2361
  • MSC: Primary 20G35; Secondary 20G05
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1283542-7
  • MathSciNet review: 1283542