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VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20201015T090737Z
DTSTART:20201020T120000Z
DTEND:20201020T130000Z
SUMMARY:Manchester Algebra Seminar - Olivier Dudas - Macdonald polynomial
s and decomposition numbers for finite unitary groups
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}b156-kgalkg
d4-3fwz27
DESCRIPTION:Speaker: Olivier Dudas - Université de Paris VII \n\nTitle:
Macdonald polynomials and decomposition numbers for finite unitary grou
ps\n\nAbstract: (work in progress with R. Rouquier) I will present a com
putational (yet conjectural) method to determine some decomposition matr
ices 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 group
s of Lie type is a very challenging problem.\n\nIn this talk I will focu
s 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) co
ming 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 evide
nce suggests that the case of finite unitary groups is obtained by takin
g a suitable square root of that equivalence\, which encodes the relatio
n between GU(n\,q) and GL(n\,-q).\n\nTime: 1pm\n\n\nPlace: Zoom
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Zoom - online\, Alan Turing Building\, Manchester
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