{"paper":{"title":"Simple $\\mathfrak{sl}(V)$-modules which are free over an abelian subalgebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Nilsson","submitted_at":"2019-03-22T10:19:35Z","abstract_excerpt":"Let $\\mathfrak{p}$ be a parabolic subalgebra of $\\mathfrak{sl}(V)$ of maximal dimension and let $\\mathfrak{n} \\subset \\mathfrak{p}$ be the corresponding nilradical. In this paper we classify the set of $\\mathfrak{sl}(V)$-modules whose restriction to $U(\\mathfrak{n})$ is free of rank $1$. It turns out that isomorphism classes of such modules are parametrized by polynomials in $\\dim V-1$ variables. We determine the submodule structure for these modules and we show that they generically are simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09431","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"}