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SUMMARY:A proof of De Concini-Kac-Procesi conjecture and Lusztig's partiti
 on - Alexey Sevastyanov\, Aberdeen
DTSTART:20151125T163000Z
DTEND:20151125T173000Z
UID:TALK60997@talks.cam.ac.uk
CONTACT:David Stewart
DESCRIPTION:In 1992 De Concini\, Kac and Procesi observed that isomorphism
  classes of irreducible representations of a quantum group at odd primitiv
 e root of unity m are parameterized by conjugacy classes in the correspond
 ing algebraic group G. They also conjectured that the dimensions of irredu
 cible representations corresponding to a given conjugacy class O are divis
 ible by m^(1/2dimO). In this talk I shall outline a proof of an improved v
 ersion of this conjecture and derive some important consequences of it rel
 ated to q-W algebras.\n\nA key ingredient of the proof are transversal sli
 ces S to the set of conjugacy classes in G. Namely\, for every conjugacy c
 lass O in G one can find a special transversal slice S such that O interse
 cts S and dim O=codim S. The construction of the slice utilizes some new c
 ombinatorics related to invariant planes for the action of Weyl group elem
 ents in the real reflection representation. The condition dim O=codim S is
  checked using some new mysterious results by Lusztig on intersection of c
 onjugacy classes in algebraic groups with Bruhat cells.\n
LOCATION:MR12
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