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CATEGORIES:Algebra seminar
SUMMARY:Macdonald polynomials and decomposition numbers fo
r finite unitary groups - Olivier Dudas (IMJ-PRG)
DTSTART:20201001T140000Z
DTEND:20201001T150000Z
UID:TALK4329AT
URL:/talk/index/4329
DESCRIPTION:(work in progress with R. Rouquier) I will present
a computational (yet conjectural) method to deter
mine some decomposition matrices for finite groups
of Lie type. These matrices encode how ordinary r
epresentations 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 challengin
g problem.\n\nIn this talk I will focus on the fin
ite general unitary group GU(n\,q). I will first e
xplain how one can produce a "natural" self-equiva
lence in the case of GL(n\,q) coming from the topo
logy of the Hilbert scheme of the complex plane .
The combinatorial part of this equivalence is rela
ted to Macdonald's theory of symmetric functions a
nd gives (q\,t)-decomposition numbers. The evidenc
e suggests that the case of finite unitary groups
is obtained by taking a suitable square root of th
at equivalence\, which encodes the relation betwee
n GU(n\,q) and GL(n\,-q).
LOCATION:https://bham-ac-uk.zoom.us/j/92610684996?pwd=K2FKV
2dpczhXSUdvUllqNnlYMVlEUT09
CONTACT:Lewis Topley
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