{"paper":{"title":"The orthogonal Weingarten formula in compact form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Teodor Banica","submitted_at":"2009-06-25T13:54:12Z","abstract_excerpt":"We present a compact formulation of the orthogonal Weingarten formula, with the traditional quantity $I(i_1,...,i_{2k}:j_1,...,j_{2k}) = \\int_{O_n}u_{i_1j_1} ... u_{i_{2k}j_{2k}} du$ replaced by the more advanced quantity $I(a)=\\int_{O_n}\\Pi u_{ij}^{a_{ij}} du$, depending on a matrix of exponents $a\\in M_n(\\mathbb N)$. Among consequences, we establish a number of basic facts regarding the integrals $I(a)$: vanishing conditions, possible poles, asymptotic behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.4694","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"}