SPEAKER: Pavel Etingof
TITLE: Equivariant D-modules on the nilcone and representations of the rational Cherednik algebra in type A
ABSTRACT Irreducible equivariant D-modules on a simple complex Lie algebra supported on its nilcone are parametrized by pairs, consisting of a nilpotent orbit and an irreducible local system on it. Such a D-module splits into a direct sum of irreducible representations of the Lie algebra, and the multiplicity spaces are graded by the eigenvalues of the Euler operator, so that the homogeneous pieces are finite dimensional. The generating function of these dimensions may be called the character of this D-module, and it is an interesting problem to calculate it. I will explain how this problem can be addressed in type A by utilizing the representation theory of the rational Cherednik algebra. This is joint work with B. Enriquez and D. Calaque.