{"paper":{"title":"On a relation between the basic representation of the affine Lie algebra $\\widehat\\sl$ and a Schur--Weyl representation of the infinite symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anatoly Vershik, Natalia Tsilevich","submitted_at":"2014-03-06T20:14:47Z","abstract_excerpt":"We prove that there is a natural grading-preserving isomorphism of $\\sl$-modules between the basic module of the affine Lie algebra $\\widehat\\sl$ (with the homogeneous grading) and a Schur--Weyl module of the infinite symmetric group $\\sinf$ with a grading defined through the combinatorial notion of the major index of a Young tableau, and study the properties of this isomorphism. The results reveal new and deep interrelations between the representation theory of $\\widehat\\sl$ and the Virasoro algebra on the one hand, and the representation theory of $\\sinf$ and the related combinatorics on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1558","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"}