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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