The $p$-adic groups and their Weyl groups

GAP Seminar

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Ping Xu, Nigel Higson, Mathieu Stienon, Matthew Peddie.

Speaker: Xuhua He, University of Maryland

Abstract: In a 1957 paper, Tits explained the analogy between the symmetric group $S_n$ and the general linear group over a finite field $\mathbb F_q$ and indicated that $S_n$ should be regarded as the general linear group over $\mathbb F_1$, the field of one element. Following Tits' philosophy, we would like to regard the affine Weyl groups as the reductive group over $\mathbb Q_1$, the $1$-adic field. Although it is still premature to develop the theory of $1$-adic field at the current stage, we do have a fairly good understanding on the conjugacy classes of the affine Weyl groups, together with the length function on it, and such knowledge allows us to reveal a great part of the structure of the conjugacy classes of $p$-adic groups. I will explain how this idea may be used in representation theory and in arithmetic geometry.

Room Reservation Information

Room Number: 106 McAllister

Date: 01/22/2019

Time: 2:30pm - 3:30pm