Kleshchev’s decomposition numbers for diagrammatic Cherednik algebras

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.

Cherednik Algebras for Algebraic Curves

For any algebraic curve C and n ≥ 1, P. Etingof introduced a ‘global’ Cherednik algebra as a natural deformation of the cross product D(Cn)⋊Sn, of the algebra of differential operators on Cn and the symmetric group. We provide a construction of the global Cherednik algebra in terms of quantum Hamiltonian reduction. We study a category of character Dmodules on a representation scheme associated ...

Abelian Localization for Cherednik Algebras

The goal of this talk is to prove an analog of the Beilinson-Bernstein localization theorem for Cherednik algebras. Strictly speaking we will only do this for categories O, in fact, the localization theorem for all modules follows from here. Let us recall the notation and some definitions. We consider the reflection representation h of the symmetric group Sn. By X we denote the “normalized” Hil...

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.

Lecture Notes on Cherednik Algebras