{"paper":{"title":"Demazure submodules of level-zero extremal weight modules and specializations of Macdonald polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Daisuke Sagaki, Satoshi Naito","submitted_at":"2014-04-09T11:14:06Z","abstract_excerpt":"In this paper, we give a characterization of the crystal bases $\\mathcal{B}_{x}^{+}(\\lambda)$, $x \\in W_{\\mathrm{af}}$, of Demazure submodules $V_{x}^{+}(\\lambda)$, $x \\in W_{\\mathrm{af}}$, of a level-zero extremal weight module $V(\\lambda)$ over a quantum affine algebra $U_{q}$, where $\\lambda$ is an arbitrary level-zero dominant integral weight, and $W_{\\mathrm{af}}$ denotes the affine Weyl group. This characterization is given in terms of the initial direction of a semi-infinite Lakshmibai-Seshadri path, and is established under a suitably normalized isomorphism between the crystal basis $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2436","kind":"arxiv","version":3},"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"}