Supports of simple modules in cyclotomic Cherednik categories O

Abstract

The goal of this paper is to compute the supports of simple modules in the categories $\mathcal{O}$ for the rational Cherednik algebras associated to groups $G(\ell,1,n)$. For this we compute some combinatorial maps on the set of simples: wall-crossing bijections and a certain $\mathfrak{sl}_\infty$-crystal associated to a Heisenberg algebra action on a Fock space.