Publication date:
9 July 2017
Source:Advances in Mathematics, Volume 314
Author(s): Stewart Wilcox
We first consider the rational Cherednik algebra corresponding to the action of a finite group on a complex variety, as defined by Etingof. We define a category of representations of this algebra which is analogous to “category $\mathcal{O}$” for the rational Cherednik algebra of a vector space. We generalise to this setting Bezrukavnikov and Etingof's results about the possible support sets of such representations. Then we focus on the case of $S_n$ acting on ${\mathbb{C}}^n$, determining which irreducible modules in this category have which support sets. We also show that the category of representations with a given support, modulo those with smaller support, is equivalent to the category of finite dimensional representations of a certain Hecke algebra.