Semi-infinite Lakshmibai--Seshadri paths and level-zero extremal weight modules over twisted quantum affine algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917210192084992 |
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| author | Adachi, Shohei Koike, Hayato |
| author_facet | Adachi, Shohei Koike, Hayato |
| contents | In this paper, we study level-zero extremal weight modules over twisted quantum affine algebras. To this end, we introduce semi-infinite Lakshmibai--Seshadri paths associated with a level-zero dominant integral weight $λ$. We then show that the set $\tfrac{\infty}{2}\mathrm{LS}(λ)$ of semi-infinite LS paths of shape $λ$ is isomorphic, as a crystal, to the crystal basis $\mathcal{B}(λ)$ of the corresponding level-zero extremal weight module $V(λ)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semi-infinite Lakshmibai--Seshadri paths and level-zero extremal weight modules over twisted quantum affine algebras Adachi, Shohei Koike, Hayato Quantum Algebra Representation Theory 17B37 (Primary), 17B67, 81R50, 81R10 (Secondary) In this paper, we study level-zero extremal weight modules over twisted quantum affine algebras. To this end, we introduce semi-infinite Lakshmibai--Seshadri paths associated with a level-zero dominant integral weight $λ$. We then show that the set $\tfrac{\infty}{2}\mathrm{LS}(λ)$ of semi-infinite LS paths of shape $λ$ is isomorphic, as a crystal, to the crystal basis $\mathcal{B}(λ)$ of the corresponding level-zero extremal weight module $V(λ)$. |
| title | Semi-infinite Lakshmibai--Seshadri paths and level-zero extremal weight modules over twisted quantum affine algebras |
| topic | Quantum Algebra Representation Theory 17B37 (Primary), 17B67, 81R50, 81R10 (Secondary) |
| url | https://arxiv.org/abs/2601.13016 |