Number Theory Seminar: Radhika Ganapathy

Abstract:

Deligne and Kazhdan used the notion of close local fields to establish a way of analyzing representations of Galois groups and Algebraic groups over fields of characteristic p, using information about corresponding representations in characteristic 0.  I will first explain this theory and some related results. Then I will state our results on the extension of Kazhdan's and Howe's work on Hecke Algebra isomorphims. I will also explain how this extension has enabled us to generalize Lemaire's work on generic representations of Gl_n(F) over close local fields.