Unbounded $\mathfrak{sl}_3$-laminations around punctures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909192149794816 |
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| author | Ishibashi, Tsukasa Kano, Shunsuke |
| author_facet | Ishibashi, Tsukasa Kano, Shunsuke |
| contents | We continue to study the unbounded $\mathfrak{sl}_3$-laminations [IK22], with a focus on their structures at punctures. A key ingredient is their relation to the root data of $\mathfrak{sl}_3$. After giving a classification of signed $\mathfrak{sl}_3$-webs around a puncture, we describe the tropicalization of the Goncharov--Shen's Weyl group action in detail. We also clarify the relationship with several other approaches by Shen--Sun--Weng [SSW23] and Fraser--Pylyavskyy [FP21]. Finally, we discuss a formulation of unbounded $\mathfrak{g}$-laminations for a general semisimple Lie algebra $\mathfrak{g}$ in brief. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18236 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unbounded $\mathfrak{sl}_3$-laminations around punctures Ishibashi, Tsukasa Kano, Shunsuke Representation Theory Geometric Topology Quantum Algebra We continue to study the unbounded $\mathfrak{sl}_3$-laminations [IK22], with a focus on their structures at punctures. A key ingredient is their relation to the root data of $\mathfrak{sl}_3$. After giving a classification of signed $\mathfrak{sl}_3$-webs around a puncture, we describe the tropicalization of the Goncharov--Shen's Weyl group action in detail. We also clarify the relationship with several other approaches by Shen--Sun--Weng [SSW23] and Fraser--Pylyavskyy [FP21]. Finally, we discuss a formulation of unbounded $\mathfrak{g}$-laminations for a general semisimple Lie algebra $\mathfrak{g}$ in brief. |
| title | Unbounded $\mathfrak{sl}_3$-laminations around punctures |
| topic | Representation Theory Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2404.18236 |