{"id":"W3165440316","doi":"10.1016/j.aim.2022.108536","title":"Schur functions in noncommuting variables","year":2022,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Noncommutative geometry; Schur algebra; Symmetric function; Schur product theorem; Schur's theorem; Schur's lemma; Schur polynomial; Schur complement; Schur decomposition; Pure mathematics; Combinatorics; Algebra over a field; Macdonald polynomials; Orthogonal polynomials","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001832732,0.001687086,0.001301036,0.005103914,0.00268032,0.004467667,0.001500295,0.001173505,0.01172453],"category_scores_gemma":[0.003150906,0.0007104665,0.0009028182,0.003757538,0.005804351,0.008604713,0.002692345,0.003119466,0.001909077],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001517181,"about_ca_system_score_gemma":0.0009963205,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009090084,"about_ca_topic_score_gemma":0.001199023,"domain_scores_codex":[0.9989129,0.0003772166,0.00005793853,0.000151457,0.0003270664,0.0001732783],"domain_scores_gemma":[0.998276,0.0007841735,0.0002105536,0.0001667112,0.0002880101,0.0002746174],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005604369,0.000005776797,0.00002549015,0.00001011958,0.000002114299,0.0000259006,0.00006956651,0.0001062799,0.00009908038,0.9982351,0.0002869801,0.00112781],"study_design_scores_gemma":[0.000005426017,0.000006646143,0.00008404929,0.000004788416,0.000003096851,0.00004121459,0.00003620304,0.0009518898,0.0001373566,0.9970924,0.001629426,0.000007561198],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4313857,0.005797371,0.219289,0.005127455,0.003042408,0.0001112614,0.0004715603,0.0004287776,0.3343464],"genre_scores_gemma":[0.8984224,0.002362034,0.02324641,0.0007254039,0.002337196,0.0001060005,0.0002333219,0.000195477,0.07237191],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01172453,"threshold_uncertainty_score":0.03922248,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02767993725763277,"score_gpt":0.3257091046721031,"score_spread":0.2980291674144703,"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."}}