University of Birmingham > Talks@bham > Algebra seminar > Macdonald polynomials and decomposition numbers for finite unitary groups

## Macdonald polynomials and decomposition numbers for finite unitary groupsAdd to your list(s) Download to your calendar using vCal - Olivier Dudas (IMJ-PRG)
- Thursday 01 October 2020, 15:00-16:00
- https://bham-ac-uk.zoom.us/j/92610684996?pwd=K2FKV2dpczhXSUdvUllqNnlYMVlEUT09.
If you have a question about this talk, please contact Lewis Topley. (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). This talk is part of the Algebra seminar series. ## This talk is included in these lists:- Algebra seminar
- School of Mathematics events
- https://bham-ac-uk.zoom.us/j/92610684996?pwd=K2FKV2dpczhXSUdvUllqNnlYMVlEUT09
Note that ex-directory lists are not shown. |
## Other listsPostgraduate Algebra Seminar Algebra Reading Group on Sporadic Groups Metallurgy & Materials – Tech Entrepreneurship Seminar Series## Other talksWaveform modelling and the importance of multipole asymmetry in Gravitational Wave astronomy TBA TBA Life : it’s out there, but what and why ? TBA Proofs of Turán's theorem |