Monomial realizations and LS paths of fundamental representations for rank $2$ Kac-Moody algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929439957319680 |
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| author | Kanakubo, Yuki |
| author_facet | Kanakubo, Yuki |
| contents | For a Kac-Moody algebra $\mathfrak{g}$ of rank $2$ and a fundamental weight $λ$, we explicitly give an isomorphism between the set of Lakshmibai-Seshadri paths $\mathbb{B}(λ)$ and monomial realization $\mathcal{M}(λ)$. As an application, we also give an explicit form of monomial realization $\mathcal{M}(λ)$ in terms of Weyl groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19622 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monomial realizations and LS paths of fundamental representations for rank $2$ Kac-Moody algebras Kanakubo, Yuki Quantum Algebra Combinatorics Representation Theory For a Kac-Moody algebra $\mathfrak{g}$ of rank $2$ and a fundamental weight $λ$, we explicitly give an isomorphism between the set of Lakshmibai-Seshadri paths $\mathbb{B}(λ)$ and monomial realization $\mathcal{M}(λ)$. As an application, we also give an explicit form of monomial realization $\mathcal{M}(λ)$ in terms of Weyl groups. |
| title | Monomial realizations and LS paths of fundamental representations for rank $2$ Kac-Moody algebras |
| topic | Quantum Algebra Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2407.19622 |