Finite dimensional quotients of Hecke algebras

TL;DR

This paper proves that for complex reflection groups, the Hecke algebra has a maximal finite-dimensional quotient with dimension equal to the group's order, supporting a conjecture using Rational Cherednik algebra categories.

Contribution

It establishes the existence and dimension of the maximal finite-dimensional quotient of Hecke algebras for complex reflection groups, advancing the Broué-Malle-Rouquier conjecture.

Findings

Maximal finite-dimensional quotient of Hecke algebra exists

Dimension of quotient equals the order of the reflection group

Supports a weak version of the Broué-Malle-Rouquier conjecture

Abstract

Let W be a complex reflection group. We prove that there is the 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 Brou\'e-Malle-Rouquier conjecture from 1998. The proof is based on categories O for Rational Cherednik algebras.