Abstract:
The rational Cherednik algebra associated with a complex reflection group W acting in a vector space V is a versal deformation of the algebra generated by W and differential operators on V. Its representation theory is closely connected to the geometry of the action of W of V. The classification of the finite dimensional representations of the rational Cherednik algebra is a long-standing open problem. In the case of a real reflection group, Etingof has proved that part of this classification may be done using the Macdonald-Mehta integral and the b-function of the discriminant for W. We explain a new proof of Etingof's criterion that extends it to all complex reflection groups.

This is joint work with Daniel Juteau.