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arXiv · 2209.06610

On the centre of Iwahori-Hecke algebras

Timothée Marquis·Sven Raum
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Abstract

We prove triviality of the centre of arbitrary Hecke algebras of irreducible non-finite non-affine type. This result is obtained as a consequence of the following structure result for conjugacy classes of the underlying Coxeter groups. If $W$ is any infinite irreducible Coxeter group and $w \in W$ is a nontrivial element that is assumed not be a translation in case $W$ is affine, then there is an infinite sequence of conjugates of $w$ by Coxeter generators whose length is non-decreasing and tends to infinity.

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Timothée Marquis, Sven Raum. 2022-09-14. On the centre of Iwahori-Hecke algebras. https://doi.org/10.1016/j.jalgebra.2023.06.010

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