Algebra & Number Theory

Finite-dimensional quotients of Hecke algebras

Ivan Losev

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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.

Article information

Algebra Number Theory, Volume 9, Number 2 (2015), 493-502.

Received: 13 August 2014
Accepted: 18 February 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20C08: Hecke algebras and their representations
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 16G99: None of the above, but in this section

Hecke algebras rational Cherednik algebras categories $\mathcal O$ KZ functor


Losev, Ivan. Finite-dimensional quotients of Hecke algebras. Algebra Number Theory 9 (2015), no. 2, 493--502. doi:10.2140/ant.2015.9.493.

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