Braid group actions on grassmannians and extended crystals of type $A$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909346813706240 |
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| author | Li, Jian-Rong Park, Euiyong |
| author_facet | Li, Jian-Rong Park, Euiyong |
| contents | Let $σ_i$ be the braid actions on infinite Grassmannian cluster algebras induced from Fraser's braid group actions. Let $\mathsf{T}_i$ be the braid group actions on (quantum) Grothendieck rings of Hernandez-Leclerc category ${\mathscr C}_\mathfrak{g}^0$ of affine type $A_n^{(1)}$, and $\mathsf{R}_i$ the braid group actions on the corresponding extended crystals. In the paper, we prove that the actions $σ_i$ coincide with the braid group actions $\mathsf{T}_i$ and $\mathsf{R}_i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Braid group actions on grassmannians and extended crystals of type $A$ Li, Jian-Rong Park, Euiyong Representation Theory Algebraic Geometry Group Theory Let $σ_i$ be the braid actions on infinite Grassmannian cluster algebras induced from Fraser's braid group actions. Let $\mathsf{T}_i$ be the braid group actions on (quantum) Grothendieck rings of Hernandez-Leclerc category ${\mathscr C}_\mathfrak{g}^0$ of affine type $A_n^{(1)}$, and $\mathsf{R}_i$ the braid group actions on the corresponding extended crystals. In the paper, we prove that the actions $σ_i$ coincide with the braid group actions $\mathsf{T}_i$ and $\mathsf{R}_i$. |
| title | Braid group actions on grassmannians and extended crystals of type $A$ |
| topic | Representation Theory Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2410.09458 |