Finite-dimensional quotients of Hecke algebras

Losev, Ivan

doi:10.2140/ant.2015.9.493

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Finite-dimensional quotients of Hecke algebras

Ivan Losev

Vol. 9 (2015), No. 2, 493–502

DOI: 10.2140/ant.2015.9.493

Abstract

Let $W$ be a complex reflection group. We prove that there is a maximal finite-dimensional quotient of the Hecke algebra $ℋ_{q} (W)$ 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

Vol. 9, No. 2, 2015