Unipotent quantum coordinate ring and minuscule prefundamental representations: twisted case
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917127100825600 |
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| author | Jang, Il-Seung |
| author_facet | Jang, Il-Seung |
| contents | We study the prefundamental modules $L_{s,a}^{\pm}$ over the Borel subalgebras of the twisted quantum loop algebras, which are introduced by Wang. A character formula for $L_{s,a}^{\pm}$ is obtained from that for the prefundamental modules over the untwisted quantum loop algebras by applying a character folding map. This allows us to realize minuscule prefundamental modules $L_{s,a}^{\pm}$ for types $A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ in terms of the unipotent quantum coordinate ring associated with the $s$-th level $0$ fundamental weight, where $s = 1$ for type $A_{2n-1}^{(2)}$ and $s = n$ for type $D_{n+1}^{(2)}$. This result is a continuation of the realization of (co)minuscule prefundamental modules established by earlier works [J-Kwon-Park, Int. Math. Res. Not., 2023] and [J-Kwon-Park, J. Algebra, 2025]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unipotent quantum coordinate ring and minuscule prefundamental representations: twisted case Jang, Il-Seung Representation Theory Quantum Algebra 17B37, 17B67, 17B10, 05E10 We study the prefundamental modules $L_{s,a}^{\pm}$ over the Borel subalgebras of the twisted quantum loop algebras, which are introduced by Wang. A character formula for $L_{s,a}^{\pm}$ is obtained from that for the prefundamental modules over the untwisted quantum loop algebras by applying a character folding map. This allows us to realize minuscule prefundamental modules $L_{s,a}^{\pm}$ for types $A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ in terms of the unipotent quantum coordinate ring associated with the $s$-th level $0$ fundamental weight, where $s = 1$ for type $A_{2n-1}^{(2)}$ and $s = n$ for type $D_{n+1}^{(2)}$. This result is a continuation of the realization of (co)minuscule prefundamental modules established by earlier works [J-Kwon-Park, Int. Math. Res. Not., 2023] and [J-Kwon-Park, J. Algebra, 2025]. |
| title | Unipotent quantum coordinate ring and minuscule prefundamental representations: twisted case |
| topic | Representation Theory Quantum Algebra 17B37, 17B67, 17B10, 05E10 |
| url | https://arxiv.org/abs/2512.02946 |