{"id":"W2325964884","doi":"10.4064/bc89-0-14","title":"Jucys-Murphy elements and the unitary Weingarten function","year":2010,"lang":"en","type":"article","venue":"Banach Center Publications","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":31,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Unitary state; Connection (principal bundle); Function (biology); Pure mathematics; Mathematics; Group (periodic table); Algebra over a field; Physics; Geometry; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006137531,0.00008379116,0.00007148828,0.00009932239,0.0003740101,0.0002773814,0.0006258353,0.00003452614,0.00009833935],"category_scores_gemma":[0.00005484923,0.00005812621,0.00003915929,0.0003447788,0.0001085538,0.0006161381,0.0002044867,0.000204699,0.00005420946],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006590089,"about_ca_system_score_gemma":0.0000289403,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001807989,"about_ca_topic_score_gemma":0.00003252811,"domain_scores_codex":[0.999207,0.00009019165,0.0001692059,0.0002321952,0.0001237618,0.0001776129],"domain_scores_gemma":[0.9990215,0.0000869283,0.00006764045,0.0006437476,0.00009732787,0.00008285885],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.000003869256,0.00006124,0.001465239,0.000002354926,0.00001867284,2.076204e-7,0.0001462094,3.8529e-7,0.00006516202,0.9682761,0.006169321,0.02379128],"study_design_scores_gemma":[0.001739937,0.00003211302,0.035343,0.00000477408,0.000022423,0.00004616876,0.00005234002,0.02577545,0.00004162053,0.0777859,0.8589494,0.0002068637],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05481029,0.0001975225,0.7509027,0.09900551,0.002973411,0.00119567,0.00005029496,0.000765733,0.09009894],"genre_scores_gemma":[0.9842912,0.00001587211,0.01040828,0.001961734,0.0002186177,0.0001158534,0.00004821693,0.00000939697,0.002930839],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9294809,"threshold_uncertainty_score":0.2876621,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007117282343164081,"score_gpt":0.2159249374556779,"score_spread":0.2088076551125138,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}