#### Vol. 9, No. 2, 2015

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editors' Interests Submission Guidelines Submission Form Editorial Login Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
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 ${\mathsc{ℋ}}_{q}\left(W\right)$ 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 $\mathsc{O}$ for rational Cherednik algebras.

##### Keywords
Hecke algebras, rational Cherednik algebras, categories $\mathcal O$, KZ functor
##### Mathematical Subject Classification 2010
Primary: 20C08
Secondary: 20F55, 16G99