{"paper":{"title":"\\v{S}apovalov elements for simple Lie algebras and basic classical simple Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Ian M. Musson","submitted_at":"2012-09-03T18:57:00Z","abstract_excerpt":"Let $M(\\gl)$ be a Verma module for a basic classical simple Lie superalgebra $\\fg \\neq G(3)$ defined using the distinguished Borel subalgebra, and let $\\gc$ be an isotropic positive root of $\\fg.$ As a special case of our first main result we show that if $\\mu, \\gl \\in \\fh^*$ with $\\gl-\\mu = \\gc$ we have $$\\dim \\Hom_{\\sfg}(M(\\mu),M(\\gl))\\le 1.$$\n  This result applies to the construction of \\v{S}apovalov elements for isotropic roots. The proof rests on a comparison with the corresponding result for a certain simple Lie algebra $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0431","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"}