q-Schur algebras and complex reflection groups, I
Representation Theory
2007-12-03 v2 Quantum Algebra
Abstract
We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to B_n(d). We prove an ``abstract'' translation principle. These results follow from the unicity of certain highest categories covering Hecke algebras. We also provide a semi-simplicity criterion for Hecke algebras of complex reflection groups.
Cite
@article{arxiv.math/0509252,
title = {q-Schur algebras and complex reflection groups, I},
author = {Raphael Rouquier},
journal= {arXiv preprint arXiv:math/0509252},
year = {2007}
}
Comments
Corrected version, 5.2.3 and 5.2.4 are new