{"paper":{"title":"Crystals, semistandard tableaux and cyclic sieving phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Euiyong Park, Young-Tak Oh","submitted_at":"2019-06-18T07:45:42Z","abstract_excerpt":"In this paper, we study a new cyclic sieving phenomenon on the set $\\mathsf{SST}_n(\\lambda)$ of semistandard Young tableaux with the cyclic action $\\mathsf{c}$ arising from its $U_q(\\mathfrak{sl}_n)$-crystal structure. We prove that if $\\lambda$ is a Young diagram with $\\ell(\\lambda) < n$ and $\\gcd( n, |\\lambda| )=1$, then the triple $\\left( \\mathsf{SST}_n(\\lambda), \\mathsf{C}, q^{- \\kappa(\\lambda)} s_\\lambda(1,q, \\ldots, q^{n-1}) \\right) $ exhibits the cyclic sieving phenomenon, where $\\mathsf{C}$ is the cyclic group generated by $\\mathsf{c}$. We further investigate a connection between $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07420","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":""},"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"}