{"paper":{"title":"On some families of modules for the current algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Matthew Bennett, Rollo Jenkins","submitted_at":"2015-08-04T23:47:54Z","abstract_excerpt":"Given a finite-dimensional module, $V$, for a finite-dimensional, complex, semi-simple Lie algebra $\\lie g$ and a positive integer $m$, we construct a family of graded modules for the current algebra $\\lie g[t]$ indexed by simple $\\CC\\lie S_m$-modules. These modules have the additional structure of being free modules of finite rank for the ring of symmetric polynomials and so can be localized to give finite-dimensional graded $\\lie g[t]$-modules. We determine the graded characters of these modules and show that if $\\lie g$ is of type $A$ and $V$ the natural representation, these graded charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00941","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"}