{"paper":{"title":"Invariants of the special orthogonal group and an enhanced Brauer category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gustav Lehrer, Ruibin Zhang","submitted_at":"2016-12-13T02:31:54Z","abstract_excerpt":"We first give a short intrinsic, diagrammatic proof of the First Fundamental Theorem of invariant theory (FFT) for the special orthogonal group $\\text{SO}_m(\\mathbb{C})$, given the FFT for $\\text{O}_m(\\mathbb{C})$. We then define, by means of a presentation with generators and relations, an enhanced Brauer category $\\widetilde{\\mathcal{B}}(m)$ by adding a single generator to the usual Brauer category $\\mathcal{B}(m)$, together with four relations. We prove that our category $\\widetilde{\\mathcal{B}}(m)$ is actually (and remarkably) {\\em equivalent} to the category of representations of $\\text{S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03998","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"}