Fixed points of DT transformations, cluster exponents and degrees of Weyl groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912477931896832 |
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| author | Germain, Antoine de Saint Lu, Jiang-Hua |
| author_facet | Germain, Antoine de Saint Lu, Jiang-Hua |
| contents | Inspired by a recent work of Y. Mizuno, we show that the DT transformations on a cluster ensemble of finite type admit unique totally positive fixed points, and that the exponents of the linearizations of the DT transformations at the fixed points are precisely the degrees of the Weyl group of the corresponding finite root system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed points of DT transformations, cluster exponents and degrees of Weyl groups Germain, Antoine de Saint Lu, Jiang-Hua Rings and Algebras Representation Theory 13F60, 17B22 Inspired by a recent work of Y. Mizuno, we show that the DT transformations on a cluster ensemble of finite type admit unique totally positive fixed points, and that the exponents of the linearizations of the DT transformations at the fixed points are precisely the degrees of the Weyl group of the corresponding finite root system. |
| title | Fixed points of DT transformations, cluster exponents and degrees of Weyl groups |
| topic | Rings and Algebras Representation Theory 13F60, 17B22 |
| url | https://arxiv.org/abs/2503.11391 |