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On isomorphisms of certain functors for Cherednik algebras

Author: Ivan Losev
Journal: Represent. Theory 17 (2013), 247-262
MSC (2010): Primary 16G99
Published electronically: May 14, 2013
MathSciNet review: 3054265
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Abstract: Bezrukavnikov and Etingof introduced some functors between the categories $\mathcal {O}$ for rational Cherednik algebras. Namely, they defined two induction functors $\mathrm {Ind}_b, \mathrm {ind}_\lambda$ and two restriction functors $\mathrm {Res}_b,\mathrm {res}_\lambda$. They conjectured that one has functor isomorphisms $\mathrm {Ind}_b\cong \mathrm {ind}_\lambda , \mathrm {Res}_b\cong \mathrm {res}_\lambda$. The goal of this paper is to prove this conjecture.

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Ivan Losev
Affiliation: Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115

Received by editor(s): January 25, 2012
Received by editor(s) in revised form: November 25, 2012
Published electronically: May 14, 2013
Additional Notes: The author was supported by the NSF grant DMS-0900907
Article copyright: © Copyright 2013 American Mathematical Society