Toshiyuki Tanisaki

Algebraic Groups and Quantum Groups

Let g be a complex simple Lie algebra, f a nilpotent element of g. We show that (1) the center of the W -algebra Wcri(g, f) associated (g, f) at the critical level coincides with the Feigin-Frenkel center of ĝ, (2) the centerless quotient Wχ(g, f) of Wcri(g, f) corresponding to an Lg-oper χ on the disc is simple, and (3) the simple quotient Wχ(g, f) is a quantization of the jet scheme of the intersection of the Slodowy slice at f with the nilpotent cone of g.

Radon transforms for quasi-equivariant D-modules on generalized flag manifolds

Abstract In this paper we deal with Radon transforms for generalized flag manifolds in the framework of quasi-equivariant D -modules. We shall follow the method employed by Baston–Eastwood and analyze the Radon transform using the Bernstein–Gelfand–Gelfand resolution and the Borel–Weil–Bott theorem. We shall determine the transform completely on the level of the Grothendieck groups. Moreover, we point out a vanishing criterion and give a sufficient condition in order that a D -module associated to an equivariant locally free O -module is transformed into an object of the same type. The case of maximal parabolic subgroups is studied in detail.

Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra

According to Kazhdan-Lusztig and Ginzburg, the Hecke algebra of an affine Weyl group is identified with the equivariant

Differential operators on quantized flag manifolds at roots of unity, II

K

D-Modules, Perverse Sheaves, and Representation Theory

-group of Steinbergs triple variety. The

Kazhdan-Lusztig conjecture for affine Lie algebras with negative level

K

Parabolic Kazhdan–Lusztig Polynomials and Schubert Varieties

-group is equipped with a filtration indexed by closed

Characters of irreducible modules with non-critical highest weights over affine Lie algebras

G

Kazhdan-Lusztig conjecture for affine Lie algebras with negative level II: Nonintegral case

-stable subvarieties of the nilpotent variety, where

Finite-dimensional representations of quantum groups

G