Cherednik algebras and differential operators on quasi-invariants

Differential operators and Cherednik algebras

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...

A Remark on Rational Cherednik Algebras and Differential Operators on the Cyclic Quiver

We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn o C`, the wreath product of the symmetric group and the cyclic group of order `, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size `. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...

A Remark on Rational Cherednik Algebras and Differential Operators on the Cyclic Quiver

We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn ≀ Cl, the wreath product of the symmetric group and the cyclic group of order l, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size l. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...

Lecture Notes on Cherednik Algebras

Cherednik algebras and Yangians

We construct a functor from the category of modules over the trigonometric (resp. rational) Cherednik algebra of type gll to the category of integrable modules of level l over a Yangian for the loop algebra sln (resp. over a subalgebra of this Yangian called the Yangian deformed double loop algebra) and we establish that it is an equivalence of categories if l + 2 < n.