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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
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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$.

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Keywords: Chevalley group, elementary subgroup, algebra, representation
Article copyright: © Copyright 1995 American Mathematical Society