Supports of representations of the rational Cherednik algebra of type A

Details Supports of representations of the rational Cherednik algebra of type A Supports of representations of the rational Cherednik algebra of type A

2010-12-12

arxiv.org/abs/1012.2585v2

Mathematics

Representation Theory

46 pages, added Proposition 3.7 and second statement of Theorem 1.8

Scientific paper

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 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 $\C^n$, 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.

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