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 listsSERENE Seminars Astrophysics Talks Series Computer Security Seminars## Other talksProvably Convergent Plug-and-Play Quasi-Newton Methods for Imaging Inverse Problems TBC Quantum simulations using ultra cold ytterbium Sylow branching coefficients for symmetric groups Modelling uncertainty in image analysis. Geometry of alternating projections in metric spaces with bounded curvature |