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DTSTAMP:20241108T155623Z
UID:66607019abde7795333297@ist.ac.at
DTSTART:20240620T143000
DTEND:20240620T160000
DESCRIPTION:Speaker: Leonardo Patimo\nhosted by Tamas Hausel\nAbstract: One
of the most fundamental problems in representation theory is computing th
e dimensions of the weight spaces of the irreducible representations of gr
oups. For reductive groups (such as GL_n(C))\, many combinatorial models a
ddress this question\, for example by counting the number of semistandard
tableaux.The dimensions of the weight spaces of irreducible representation
s of reductive groups have a natural q-deformation\, known as the Kostka-F
oulkes polynomials. However\, finding combinatorial statistics that expres
s these polynomials remains a long-standing open problem in algebraic comb
inatorics\, which has only been solved for type A. We develop a new approa
ch based on the geometry of the affine Grassmannian\, constructing the cha
rge in terms of the associated crystal graph. This approach not only recov
ers the results of Lascoux and Schtzenberger in type A geometrically but a
lso provides a framework to find charge statistics in general.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
)\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Leonardo Patimo: A geometric approach to the charge statistics
URL:https://talks-calendar.ista.ac.at/events/5044
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