2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143290We 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.Corrected version, 5.2.3 and 5.2.4 are newRepresentation TheoryQuantum Algebratext