On category O for cyclotomic rational Cherednik algebras
Abstract
We study equivalences for category O_p of the rational Cherednik algebras H_p of type G_l(n) = \mu_l^n\rtimes S_n: a highest weight equivalence between O_p and O_{\sigma(p)} for \sigma\in S_l and an action of S_l on a nonempty Zariski open set of parameters p; a derived equivalence between O_p and O_{p'} whenever p and p' have integral difference; a highest weight equivalence between O_p and a parabolic category O for the general linear group, under a nonrationality assumption on the parameter p. As a consequence, we confirm special cases of conjectures of Etingof and of Rouquier.
 Publication:

arXiv eprints
 Pub Date:
 September 2011
 DOI:
 10.48550/arXiv.1109.2315
 arXiv:
 arXiv:1109.2315
 Bibcode:
 2011arXiv1109.2315G
 Keywords:

 Mathematics  Representation Theory;
 16G99
 EPrint:
 61 pages