A combinatorial model for representations of rational Cherednik algebras

The rational Cherednik algebra of a complex reflection group is a certain algebra with triangular decomposition, whose corresponding "category O" has irreducible modules in bijection with the irreducible modules for the underlying group. Fundamental questions about the structure of these irreducible modules include:

We propose a combinatorial model for answering these questions for the infinite series G(r,p,n) of complex reflection groups. In this talk we will focus on the case of the groups G(r,1,2), where the drawings are easier to understand but the results are quite typical.