{"paper":{"title":"\\vS{a}povalov elements and the Jantzen sum formula for contragredient Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ian M. Musson","submitted_at":"2017-10-28T21:09:19Z","abstract_excerpt":"If $\\mathfrak{g}$ is a contragredient Lie superalgebra and $\\gamma$ is a root of $\\mathfrak{g},$ we prove the existence and uniqueness of \\v{S}apovalov elements for $\\gamma$ and give upper bounds on the degrees of their coefficients. Then we use \\v{S}apovalov elements to define some new highest weight modules. If $X$ is a set of orthogonal isotropic roots and $\\lambda \\in \\mathfrak{h}^*$ is such that $\\lambda +\\rho$ is orthogonal to all roots in $X$, we construct a highest weight module $M^X(\\lambda)$ with character $\\epsilon^\\lambda {p}_X$. Here $p_X$ is a function that counts partitions not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10528","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"}