Generalized Gelfand-Graev representations for finite groups of Lie type

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• Matthew Clarke, Cambridge
• Friday 27 November 2009, 13:00-14:00
• MR13.

If you have a question about this talk, please contact Matthew Clarke.

This talk is about the ordinary (complex) representation theory of finite groups of Lie type. I will begin by carefully reviewing algebraic groups and finite groups of Lie type and the construction and properties of (ordinary) Gelfand-Graev representations. I will then introduce generalized Gelfand-Graev characters, which are constructed using the Lie algebra of the ambient algebraic group. Towards the end I hope to give an idea of how generalized Gelfand-Graev characters can and have been used to attack Lusztig’s conjecture and the role this plays in the determination of the character tables for finite groups of Lie type.

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

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