Seminari: Characters of Finite Reductive Groups

Giovedì 19 e Lunedì 23 Marzo 2015, ore 14:00 - Sala riunioni VII piano - Jay Taylor



Giovedì 19 e Lunedì 23 Marzo 2015 alle ore 14:00 in Sala riunioni VII piano, Jay Taylor (Marie Curie Indam Cofund fellow) terrà una serie di due seminari dal titolo "Characters of Finite Reductive Groups".

A finite reductive group G is the set of fixed points of a reductive algebraic group under a Frobenius endomorphism. Central examples of such finite groups include the matrix groups over finite fields, such as the general linear, special linear, symplectic and orthogonal groups. In 1976 Deligne and Lusztig constructed a family of virtual characters of G using the ell-adic cohomology of certain varieties known as Deligne--Lusztig varieties. In the same paper they showed that these virtual characters are often (up to sign) irreducible characters. This pivotal moment in representation theory gave a strong indication that the character theory of G and the geometry of the ambient algebraic group are intimately intertwined. In the last 40 years much has been done to further understand this relationship and to describe the irreducible characters of G. In the first part of this talk I will survey the current landscape of the ordinary character theory of finite reductive groups and highlight some of the ongoing work in this active area. In the second part of the talk I will focus more closely on the role of unipotent conjugacy classes in the representation theory of finite reductive groups. Specifically their relationship to Kawanaka's theory of generalised Gelfand-Graev representations.