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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.01306 |
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| _version_ | 1866916821155708928 |
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| author | Jung, Woo-Seok Park, Euiyong |
| author_facet | Jung, Woo-Seok Park, Euiyong |
| contents | Let $η_w$ be the quantum twist automorphism for the quantum unipotent coordinate ring $\mathrm{A}_q(\mathfrak{n}(w))$ introduced by Kimura and Oya. In this paper, we study the quantum twist automorphism $η_w$ in the viewpoint of the crystal bases theory and provide a crystal-theoretic description of $η_w$. In the case of the $*$-twisted minuscule crystals of classical finite types, we provide a combinatorial description of $η_w$ in terms of (shifted) Young diagrams. We further investigate the periodicity of $η_w$ up to a multiple of frozen variables in various setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Crystals and quantum twist automorphisms Jung, Woo-Seok Park, Euiyong Representation Theory Combinatorics 16T20, 17B37, 05E10 Let $η_w$ be the quantum twist automorphism for the quantum unipotent coordinate ring $\mathrm{A}_q(\mathfrak{n}(w))$ introduced by Kimura and Oya. In this paper, we study the quantum twist automorphism $η_w$ in the viewpoint of the crystal bases theory and provide a crystal-theoretic description of $η_w$. In the case of the $*$-twisted minuscule crystals of classical finite types, we provide a combinatorial description of $η_w$ in terms of (shifted) Young diagrams. We further investigate the periodicity of $η_w$ up to a multiple of frozen variables in various setting. |
| title | Crystals and quantum twist automorphisms |
| topic | Representation Theory Combinatorics 16T20, 17B37, 05E10 |
| url | https://arxiv.org/abs/2507.01306 |