q-Schur algebras and complex reflection groups, I

2005/09/12 by Rouquier, Raphael · 2 citations
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0509252

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.

Cited by

• On the functor relating Harish-Chandra bimodules and Soergel bimodules
• On the structure of Schur algebras S(p, 2p) in odd characteristic

Related

• Extensions of the rational Cherednik algebra and generalized KZ functors
• Hecke algebras and symplectic reflection algebras
• Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras
• On q-Schur algebras corresponding to Hecke algebras of type B
• Unitary representations of Hecke algebras of complex reflection groups