On isomorphisms of certain functors for Cherednik algebras

TL;DR

This paper proves a conjecture by Bezrukavnikov and Etingof that certain induction and restriction functors between categories O for rational Cherednik algebras are isomorphic, clarifying their relationship.

Contribution

It establishes the isomorphism between induction and restriction functors in categories O for rational Cherednik algebras, confirming a conjecture by Bezrukavnikov and Etingof.

Findings

Proves the isomorphism of induction functors.

Proves the isomorphism of restriction functors.

Confirms the conjecture by Bezrukavnikov and Etingof.

Abstract

Bezrukavnikov and Etingof introduced some functors between the categories O for rational Cherednik algebras. Namely, they defined two induction functors Ind_b, ind_\lambda and two restriction functors Res_b,res_\lambda. They conjectured that one has functor isomorphisms $Ind_b\cong ind_\lambda, Res_b\cong res_\lambda$. The goal of this paper is to prove this conjecture.