{"paper":{"title":"Crystals and quantum twist automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Euiyong Park, Woo-Seok Jung","submitted_at":"2025-07-02T02:47:08Z","abstract_excerpt":"Let $\\eta_w$ 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 $\\eta_w$ in the viewpoint of the crystal bases theory and provide a crystal-theoretic description of $\\eta_w$. In the case of the $*$-twisted minuscule crystals of classical finite types, we provide a combinatorial description of $\\eta_w$ in terms of (shifted) Young diagrams. We further investigate the periodicity of $\\eta_w$ up to a multiple of frozen variables in various setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.01306","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.01306/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}