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SUMMARY:Olivier Dudas (CNRS)
DTSTART:20200930T203000Z
DTEND:20200930T213000Z
DTSTAMP:20260423T052333Z
UID:MITLie/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/10/">
 Macdonald polynomials and decomposition numbers for finite unitary groups<
 /a>\nby Olivier Dudas (CNRS) as part of MIT Lie groups seminar\n\nLecture 
 held in 2-142.\n\nAbstract\n(work in progress with R. Rouquier) In this ta
 lk I will present a computational (yet conjectural) method to determine so
 me decomposition matrices for finite groups of Lie type. I will first expl
 ain how one can produce a "natural" self-equivalence in the case of $\\mat
 hrm{GL}_n(q)$ 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 b
 y taking a suitable square root of that equivalence.\n
LOCATION:https://researchseminars.org/talk/MITLie/10/
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