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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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Table of 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.