{"paper":{"title":"Invariants of the orthosymplectic Lie superalgebra and super Pfaffians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"G.I. Lehrer, R.B. Zhang","submitted_at":"2015-07-06T05:34:31Z","abstract_excerpt":"Given a complex orthosymplectic superspace $V$, the orthosymplectic Lie superalgebra $\\mathfrak {osp}(V)$ and general linear algebra ${\\mathfrak {gl}}_N$ both act naturally on the coordinate super-ring $\\mathcal{S}(N)$ of the dual space of $V\\otimes{\\mathbb C}^N$, and their actions commute. Hence the subalgebra $\\mathcal{S}(N)^{\\mathfrak {osp}(V)}$ of $\\mathfrak {osp}(V)$-invariants in $\\mathcal{S}(N)$ has a ${\\mathfrak {gl}}_N$-module structure. We introduce the space of super Pfaffians as a simple ${\\mathfrak {gl}}_N$-submodule of $\\mathcal{S}(N)^{\\mathfrak {osp}(V)}$, give an explicit formu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01329","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"}