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q-Schur algebras and complex reflection groups, I

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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https://hal.archives-ouvertes.fr/hal-00008615
Contributor : Raphael Rouquier <>
Submitted on : Monday, December 3, 2007 - 6:23:12 PM
Last modification on : Wednesday, December 9, 2020 - 3:16:37 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 2:58:01 PM

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Raphael Rouquier. q-Schur algebras and complex reflection groups, I. 2007. ⟨hal-00008615v2⟩

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