CHEREDNIK ALGEBRAS AND ZHELOBENKO OPERATORS

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...

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.

Rational Cherednik algebras

We survey a number of results about rational Cherednik algebra representation theory and its connection to symplectic singularities and their resolutions. Mathematics Subject Classification (2000). Primary 16G, 17B; Secondary 20C, 53D.

Triple groups and Cherednik algebras

The goal of this paper is to define a new class of objects which we call triple groups and to relate them with Cherednik's double affine Heeke algebras. This has as immediate consequences new descriptions of double affine Weyl and Artin groups, the double affine Heeke algebras as well as the corresponding elliptic objects. From the new descriptions we recover results of Cherednik on automorphis...

Lecture Notes on Cherednik Algebras