{"paper":{"title":"Representations of the Rook-Brauer Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Elise delMas, Tom Halverson","submitted_at":"2012-06-20T18:41:18Z","abstract_excerpt":"We study the representation theory of the rook-Brauer algebra RB_k(x), also called the partial Brauer algebra. This algebra has a basis of \"rook-Brauer\" diagrams, which are Brauer diagrams that allow for the possibility of missing edges. The Brauer, Temperley-Lieb, Motzkin, rook monoid, and symmetric group algebras are all subalgebras of the rook-Brauer algebra. We prove that RB_k(n) is the centralizer algebra of the complex orthogonal group O(n) acting on the k-fold tensor power of the sum of its 1-dimensional trivial module and its n-dimensional defining module, and thus the rook-Brauer alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4576","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"}