Generalized Gelfand--Graev representations for finite groups of Lie type

Generalized Gelfand--Graev representations for finite groups of Lie type

Wed, 02/12/2009
11:30 		Matthew Clarke (University of Cambridge) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Generalized Gelfand–Graev representations for finite groups of Lie type
This talk is about the ordinary 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 characters. 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 of finite groups of Lie type.