{"id":"W2097581076","doi":"10.1112/s0024611503014552","title":"Invariant algebras and major indices for classical Weyl groups","year":2004,"lang":"en","type":"article","venue":"Proceedings of the London Mathematical Society","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":42,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Symmetric group; Symmetric function; Hilbert–Poincaré series; Weyl group; Invariant (physics); Combinatorics; Invariant theory; Symmetric polynomial; Polynomial; Pure mathematics; Algebra over a field; Mathematical analysis","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":[0.0008720792,0.000350554,0.0007128339,0.00003145737,0.0002800048,0.00009191797,0.0006594039,0.0002727724,0.0000170065],"category_scores_gemma":[0.002448297,0.0002340408,0.0004544303,0.0003095706,0.0004709499,0.0002899959,0.0004634661,0.0003589118,0.000006105565],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001275351,"about_ca_system_score_gemma":0.00005097852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001247316,"about_ca_topic_score_gemma":6.259951e-7,"domain_scores_codex":[0.9977406,0.000006564708,0.0007749897,0.0003913309,0.000606086,0.0004804794],"domain_scores_gemma":[0.9977123,0.001000336,0.0006050799,0.000257869,0.0002635421,0.0001608897],"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":[0.00002641763,0.000379963,0.00005334617,0.002470837,0.0001100024,1.581684e-7,0.002570145,5.059562e-7,0.006598045,0.9866689,0.001043651,0.00007797773],"study_design_scores_gemma":[0.001816988,0.00013163,0.00003749492,0.0004388554,0.0002236593,0.00002801397,0.001031302,0.0003250563,0.02630098,0.9692625,0.0001381201,0.0002653959],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9713101,0.00009107163,0.02133138,0.003697599,0.0001866424,0.001999738,0.0000175638,0.0001961146,0.001169721],"genre_scores_gemma":[0.6311463,0.00002413089,0.3677482,0.0002030895,0.0002178585,0.0002417189,8.472076e-7,0.000104743,0.000313096],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3464168,"threshold_uncertainty_score":0.9543905,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0240771767849633,"score_gpt":0.2781628519861595,"score_spread":0.2540856752011962,"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."}}