Vol. 9, No. 2, 2015

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Finite-dimensional quotients of Hecke algebras

Ivan Losev

Vol. 9 (2015), No. 2, 493–502
Abstract

Let W be a complex reflection group. We prove that there is a maximal finite-dimensional quotient of the Hecke algebra q(W) of W, and that the dimension of this quotient coincides with |W|. This is a weak version of a 1998 Broué–Malle–Rouquier conjecture. The proof is based on the categories O for rational Cherednik algebras.

Keywords
Hecke algebras, rational Cherednik algebras, categories $\mathcal O$, KZ functor
Mathematical Subject Classification 2010
Primary: 20C08
Secondary: 20F55, 16G99
Milestones
Received: 13 August 2014
Accepted: 18 February 2015
Published: 5 March 2015
Authors
Ivan Losev
Department of Mathematics
Northeastern University
Boston, MA 02115
United States