On isomorphisms of certain functors for Cherednik algebras

On Isomorphisms of Certain Functors for Cherednik Algebras

Bezrukavnikov and Etingof introduced some functors between the categories O for rational Cherednik algebras. Namely, they defined two induction functors Indb, indλ and two restriction functors Resb, resλ. They conjectured that one has functor isomorphisms Indb ∼= indλ,Resb ∼= resλ. The goal of this paper is to prove this conjecture.

Monodromy of Partial Kz Functors for Rational Cherednik Algebras

1.1. Shan has proved that the categories Oc(Wn) for rational Cherednik algebras of type Wn = W (G(`, 1, n)) = Snn(μ`) with n varying, together with decompositions of the parabolic induction and restriction functors of Bezrukavnikov-Etingof, provide a categorification of an integrable s̃le Fock space representation F(m), [18]. The parameters m ∈ Z` and e ∈ N ∪ {∞} arise from the choice of paramet...

Lecture Notes on 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 ...