The University of Michigan Combinatorics Seminar
I. Cherednik posed the problem of classifying the set of unitary irreducible modules for the rational Cherednik algebra, in particular hoping for new examples of interesting infinite dimensional unitary representations.
Etingof and Stoica began the analysis, conjecturing (and partially proving) a classification in type A. This talk aims to explain how Cherednik and Suzuki's combinatorial description of rational Cherednik algebra modules leads to a proof of the Etingof-Stoica conjecture, and how to solve the analogous problem for the family G(r,p,n) of complex reflection groups, and perhaps for the Cherednik algebras attached to Weyl groups of arbitrary type.
This talk is based on work (in progress) with Charles Dunkl, on the paper "Unitary representations of rational Cherednik algebras" by Etingof and Stoica, and on the appendix I wrote to that paper.