Yang-Baxter extremal characters of wreath products of finite groups with the infinite symmetric group
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918246932807680 |
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| author | Assakaf, Hicham |
| author_facet | Assakaf, Hicham |
| contents | Let $T$ be a finite group. To a representation $π$ of $T$ and an involutive solution of the Yang-Baxter equation (an $R$-matrix) verifying the "extended" reflection equation, we associate a character and a representation of the wreath product $G:=T\wr \mathfrak{S}_\infty$. The set of extremal characters of $G$ is in bijection with a continuous set of parameters. In this article, we characterize exactly what subset of parameters does correspond to an extremal Yang-Baxter character of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Yang-Baxter extremal characters of wreath products of finite groups with the infinite symmetric group Assakaf, Hicham Representation Theory Quantum Algebra 16T25, 20C32, 20E22 Let $T$ be a finite group. To a representation $π$ of $T$ and an involutive solution of the Yang-Baxter equation (an $R$-matrix) verifying the "extended" reflection equation, we associate a character and a representation of the wreath product $G:=T\wr \mathfrak{S}_\infty$. The set of extremal characters of $G$ is in bijection with a continuous set of parameters. In this article, we characterize exactly what subset of parameters does correspond to an extremal Yang-Baxter character of $G$. |
| title | Yang-Baxter extremal characters of wreath products of finite groups with the infinite symmetric group |
| topic | Representation Theory Quantum Algebra 16T25, 20C32, 20E22 |
| url | https://arxiv.org/abs/2408.13375 |