Manchester Algebra Seminar - Olivier Dudas - Macdonald polynomials and decomposition numbers for finite unitary groups
|Starts:||13:00 20 Oct 2020|
|Ends:||14:00 20 Oct 2020|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, Current University students|
Speaker: Olivier Dudas - Université de Paris VII
Title: Macdonald polynomials and decomposition numbers for finite unitary groups
Abstract: (work in progress with R. Rouquier) I will present a computational (yet conjectural) method to determine some decomposition matrices for finite groups of Lie type. These matrices encode how ordinary representations decompose when they are reduced to a field with positive characteristic \ell. There is an algorithm to compute them for GL(n,q) when \ell is large enough, but finding these matrices for other groups of Lie type is a very challenging problem.
In this talk I will focus on the finite general unitary group GU(n,q). I will first explain how one can produce a "natural" self-equivalence in the case of GL(n,q) coming from the topology of the Hilbert scheme of the complex plane . The combinatorial part of this equivalence is related to Macdonald's theory of symmetric functions and gives (q,t)-decomposition numbers. The evidence suggests that the case of finite unitary groups is obtained by taking a suitable square root of that equivalence, which encodes the relation between GU(n,q) and GL(n,-q).
Travel and Contact Information
Zoom - online
Alan Turing Building