On the centre of Iwahori-Hecke algebras

DOI10.1016/J.JALGEBRA.2023.06.010arXiv2209.06610MaRDI QIDQ6506592

Sven Raum, Timothée Marquis

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 $winW$ 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.

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Conjugacy classes for groups (20E45) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

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