On the centre of Iwahori-Hecke algebras

Marquis, Timothée;Raum, Sven
(2024) Journal of Algebra — Vol. 656, p. 276-293 (2024)

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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 to 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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Marquis, T., & Raum, S. (2024). On the centre of Iwahori-Hecke algebras. Journal of Algebra, 656, 276-293. https://doi.org/10.1016/j.jalgebra.2023.06.010 (Original work published 2024)