On the centre of Iwahori-Hecke algebras
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929251770433536 |
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| author | Marquis, Timothée Raum, Sven |
| author_facet | Marquis, Timothée Raum, Sven |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2209_06610 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the centre of Iwahori-Hecke algebras Marquis, Timothée Raum, Sven Group Theory Rings and Algebras 20C08, 20F55, 20E45 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. |
| title | On the centre of Iwahori-Hecke algebras |
| topic | Group Theory Rings and Algebras 20C08, 20F55, 20E45 |
| url | https://arxiv.org/abs/2209.06610 |