{"paper":{"title":"Specialization of nonsymmetric Macdonald polynomials at $t=\\infty$ and Demazure submodules of level-zero extremal weight modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Daisuke Sagaki, Fumihiko Nomoto, Satoshi Naito","submitted_at":"2015-11-22T12:38:32Z","abstract_excerpt":"In this paper, we give a representation-theoretic interpretation of the specialization $E_{w_{\\circ} \\lambda} (q,\\infty)$ of the nonsymmetric Macdonald polynomial $E_{w_{\\circ} \\lambda}(q,t)$ at $t=\\infty$ in terms of the Demazure submodule $V_{w_\\circ}^{-} (\\lambda)$ of the level-zero extremal weight module $V(\\lambda)$ over a quantum affine algebra of an arbitrary untwisted type, here, $\\lambda$ is a dominant integral weight, and $w_{\\circ}$ denotes the longest element in the finite Weyl group $W$. Also, for each $x \\in W$, we obtain a combinatorial formula for the specialization $E_{x \\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07005","kind":"arxiv","version":2},"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"}