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A basis of the Gelfand-Graev algebra of a Chevalley group

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  • UserAlessandro Paolini Birmingham University
  • ClockFriday 29 November 2013, 15:00-16:00
  • HouseCMS, MR5.

If you have a question about this talk, please contact Julian Brough.

G a finite group of Lie type, B a Borel subgroup of G, and U the unipotent radical of B. The endomorphism algebra of the induced module afforded by a linear regular character of U is called Gelfand-Graev algebra. I will first recall some background about finite groups of Lie type and some representation theory. Then I move to the main feature of this talk, that is to show an explicit construction of a basis for the Gelfand-Graev algebra as a vector space, for G a Chevalley group, and to point out the efforts towards another proof of the commutativity of this algebra. In fact, the only known proof in literature cannot be used to get information about similar algebras, constructed from parabolic subgroups. I will finish briefly explaining this kind of generalization.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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