{"paper":{"title":"The spin-Brauer diagram algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Robert P. Laudone","submitted_at":"2017-04-01T03:00:48Z","abstract_excerpt":"We investigate the spin-Brauer diagram algebra, denoted ${\\bf SB}_n(\\delta)$, that arises from studying an analogous form of Schur-Weyl duality for the action of the pin group on ${\\bf V}^{\\otimes n} \\otimes \\Delta$. Here ${\\bf V}$ is the standard $N$-dimensional complex representation of ${\\bf Pin}(N)$ and $\\Delta$ is the spin representation. When $\\delta = N$ is a positive integer, we define a surjective map ${\\bf SB}_n(N) \\twoheadrightarrow {\\rm End}_{{\\bf Pin}(N)}({\\bf V}^{\\otimes n} \\otimes \\Delta)$ and show it is an isomorphism for $N \\geq 2n$. We show ${\\bf SB}_n(\\delta)$ is a cellular "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00111","kind":"arxiv","version":3},"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"}