{"paper":{"title":"The Capelli eigenvalue problem for Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hadi Salmasian, Siddhartha Sahi, Vera Serganova","submitted_at":"2018-07-19T10:51:50Z","abstract_excerpt":"For a finite dimensional unital complex simple Jordan superalgebra $J$, the Tits-Kantor-Koecher construction yields a 3-graded Lie superalgebra $\\mathfrak g_\\flat\\cong \\mathfrak g_\\flat(-1)\\oplus\\mathfrak g_\\flat(0)\\oplus\\mathfrak g_\\flat(1)$, such that $\\mathfrak g_\\flat(-1)\\cong J$. Set $V:=\\mathfrak g_\\flat(-1)^*$ and $\\mathfrak g:=\\mathfrak g_\\flat(0)$.\n  In most cases, the space $\\mathcal P(V)$ of superpolynomials on $V$ is a completely reducible and multiplicity-free representation of $\\mathfrak g$, with a decomposition $\\mathcal P(V):=\\bigoplus_{\\lambda\\in\\Omega}V_\\lambda$, where $\\left"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07340","kind":"arxiv","version":4},"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"}