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q-Schur algebras and complex reflection groups, I

Raphael Rouquier
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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.

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Raphael Rouquier. 2007-12-03. q-Schur algebras and complex reflection groups, I. https://arxiv.org/abs/math/0509252

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