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De Concini-Kac-Procesi conjecture, Schubert cells and q-W algebras
De Concini-Kac-Procesi conjecture gives a good estimate forthe dimensions of finite--dimensional non-restrictedrepresentations of quantum groups at m-th root of unity. According to DeConcini, Kac and Procesi such representations can be split into familiesparametrized by conjugacy classes in an algebraic group G, and thedimensions of representations corresponding to a conjugacy class O aredivisible by m^{dim O/2}.I shall present an approach to the proof of De Concini-Kac-Procesiconjecture based on the use of q-W algebras and Bruhat decomposition inG. It turns out that properties of representations corresponding to aconjugacy class O depend on the properties of intersection of O withcertain Bruhat cells.
- Speaker
- Alexey Sevastyanov (University of Aberdeen)