On category O for cyclotomic rational Cherednik algebras

Details On category O for cyclotomic rational Cherednik algebras On category O for cyclotomic rational Cherednik algebras

2011-09-11

arxiv.org/abs/1109.2315v2

Mathematics

Representation Theory

61 pages; v2 64 pages, new material added

Scientific paper

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 non-empty 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 non-rationality assumption on the parameter p. As a consequence, we confirm special cases of conjectures of Etingof and of Rouquier.

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