Macdonald polynomials and decomposition numbers for finite unitary groups
Olivier Dudas (CNRS)
Abstract: (work in progress with R. Rouquier) In this talk I will present a computational (yet conjectural) method to determine some decomposition matrices for finite groups of Lie type. I will first explain how one can produce a "natural" self-equivalence in the case of $\mathrm{GL}_n(q)$ coming from the topology of the Hilbert scheme of $\mathbb{C}^2$. 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.
representation theory
Audience: researchers in the topic
Series comments: Description: Research seminar on Lie groups
This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.
Organizers: | André Lee Dixon*, Ju-Lee Kim, Roman Bezrukavnikov* |
*contact for this listing |