Harish-Chandra bimodules for type A rational Cherednik algebras

Abstract

We study Harish-Chandra bimodules for the rational Cherednik algebra associated to the symmetric group Sn. In particular, we show that for any parameter c∈C, the category of Harish-Chandra Hc-bimodules admits a fully faithful embedding into the category Oc, and describe the irreducibles in the image. We also construct a duality on the category of Harish-Chandra bimodules, and in fact we do this in a greater generality of quantizations of Nakajima quiver varieties. We use this duality, along with induction and restriction functors, to describe, as an abelian category, the smallest Serre subcategory of the category of Harish-Chandra bimodules containing the regular bimodule, as well as to explicitly describe the tensor products of its irreducible objects.