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DTSTAMP:20260404T075011Z
UID:648ae47514d08087369894@ist.ac.at
DTSTART:20241017T130000
DTEND:20241017T150000
DESCRIPTION:Speaker: George Lusztig\nhosted by Tamas Hausel\nAbstract: (I) 
 Fourier transform as a linear map from L^2(R) to L^2(R) has been diagonali
 zed by Hermite in the late 1800's using Hermite polynomials.We are interes
 ted in the Fourier transform F on the C-vector space of functions on a sym
 plectic vector space over the field with two elements. We show that the fo
 llowing substitute of Hermite's resultholds: there is a remarkable C-basis
  of this vector space in which F acts as a triangular matrix.(II) Let k_p 
 be an algebraically closed field of characteristic p and let G_p be a redu
 ctive connected group over k_p of type independent of p\; let W be the Wey
 l group of G_p. We define a partition of G_p into finitely many strata. Ea
 ch stratum is a union of conjugacy classes of fixed dimension of G_p. The 
 set of strata is independent of p.It can be viewed as an enlargement of th
 e set of unipotent classes of G_p. It can be identified with the image of 
 a certain map from the set of conjugacy classes in W to the set of irreduc
 ible representations of W.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:George Lusztig: (I) Fourier transform as a triangular matrix / (II)
  Strata in reductive groups
URL:https://talks-calendar.ista.ac.at/events/5248
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