University of Cambridge > Talks.cam > Algebra and Representation Theory Seminar > A proof of De Concini-Kac-Procesi conjecture and Lusztig's partition

A proof of De Concini-Kac-Procesi conjecture and Lusztig's partition

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  • UserAlexey Sevastyanov, Aberdeen
  • ClockWednesday 25 November 2015, 16:30-17:30
  • HouseMR12.

If you have a question about this talk, please contact David Stewart.

In 1992 De Concini, Kac and Procesi observed that isomorphism classes of irreducible representations of a quantum group at odd primitive root of unity m are parameterized by conjugacy classes in the corresponding algebraic group G. They also conjectured that the dimensions of irreducible representations corresponding to a given conjugacy class O are divisible by m^(1/2dimO). In this talk I shall outline a proof of an improved version of this conjecture and derive some important consequences of it related to q-W algebras.

A key ingredient of the proof are transversal slices S to the set of conjugacy classes in G. Namely, for every conjugacy class O in G one can find a special transversal slice S such that O intersects S and dim O=codim S. The construction of the slice utilizes some new combinatorics related to invariant planes for the action of Weyl group elements in the real reflection representation. The condition dim O=codim S is checked using some new mysterious results by Lusztig on intersection of conjugacy classes in algebraic groups with Bruhat cells.

This talk is part of the Algebra and Representation Theory Seminar series.

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