{"paper":{"title":"Tensor product decomposition theorem for quantum Lakshmibai-Seshadri paths and standard monomial theory for semi-infinite Lakshmibai-Seshadri paths","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":"2018-03-02T15:15:14Z","abstract_excerpt":"Let $\\lambda$ be a (level-zero) dominant integral weight for an untwisted affine Lie algebra, and let $\\mathrm{QLS}(\\lambda)$ denote the quantum Lakshmibai-Seshadri (QLS) paths of shape $\\lambda$. For an element $w$ of a finite Weyl group $W$, the specializations at $t = 0$ and $t = \\infty$ of the nonsymmetric Macdonald polynomial $E_{w \\lambda}(q, t)$ are explicitly described in terms of QLS paths of shape $\\lambda$ and the degree function defined on them. Also, for (level-zero) dominant integral weights $\\lambda$, $\\mu$, we have an isomorphism $\\Theta : \\mathrm{QLS}(\\lambda + \\mu) \\rightarro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01727","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"}