arXiv Analytics

Sign in

arXiv:math/0509252 [math.RT]AbstractReferencesReviewsResources

q-Schur algebras and complex reflection groups, I

Raphael Rouquier

Published 2005-09-12, updated 2007-12-03Version 2

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.

Comments: Corrected version, 5.2.3 and 5.2.4 are new
Categories: math.RT, math.QA
Related articles: Most relevant | Search more
arXiv:math/0612733 [math.RT] (Published 2006-12-23, updated 2008-08-22)
Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r,p,n)
arXiv:1304.3412 [math.RT] (Published 2013-04-11, updated 2013-08-02)
Representations of Rational Cherednik algebras with minimal support and torus knots
arXiv:1505.07891 [math.RT] (Published 2015-05-29)
The polynomial representation of the type $A_{n - 1}$ rational Cherednik algebra in characteristic $p \mid n$

Links

Toolbox