Selecta Mathematica

, Volume 14, Issue 3–4, pp 397–425

Parabolic induction and restriction functors for rational Cherednik algebras

Article

DOI: 10.1007/s00029-009-0507-z

Cite this article as:
Bezrukavnikov, R. & Etingof, P. Sel. math., New ser. (2009) 14: 397. doi:10.1007/s00029-009-0507-z

Abstract.

We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation theory of rational Cherednik algebras. In particular, we prove the Gordon–Stafford theorem about Morita equivalence of the rational Cherednik algebra for type A and its spherical subalgebra, without the assumption that c is not a half-integer, which was required up to now. Also, we classify representations from category \({\mathcal{O}}\) over the rational Cherednik algebras of type A which do not contain an Sn-invariant vector, and confirm a conjecture of Okounkov and the first author on the number of such representations. We also prove that the spherical Cherednik algebra of type A is simple for − 1 < c < 0. Finally, in an appendix by the second author, we determine the reducibility loci of the polynomial representation of the trigonometric Cherednik algebra.

Mathematics Subject Classification (2000).

Primary 20C08 

Keywords.

Rational Cherednik algebra parabolic subgroup induction restriction 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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