We establish a link between two geometric approaches to the representation theory of rational Cherednik algebras of type A: one based on a noncommutative Proj construction [GS1]; the other involving quantum hamiltonian reduction of an algebra of differential operators [GG]. In the present paper, we combine these two points of view by showing that the process of hamiltonian reduction intertwines...

These are notes for a talk in the MIT-Northeastern Spring 2015 Graduate Representation Theory Seminar. The main source is [BR14].

The Matsuo–Cherednik correspondence is an isomorphism from solutions of Knizhnik–Zamolodchikov equations to eigenfunctions of generalized Calogero–Moser systems associated to Coxeter groups G and a multiplicity function m on their root systems. It is valid for generic values of the spectral parameters, in the complement of the discriminant locus. We extend the Matsuo–Cherednik correspondence co...

We establish a link between two geometric approaches to the representation theory of rational Cherednik algebras of type A: one based on a noncommutative Proj construction [GS1]; the other involving quantum hamiltonian reduction of an algebra of differential operators [GG]. In this paper, we combine these two points of view by showing that the process of hamiltonian reduction intertwines a natu...