{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008571143,0.0003410222,0.0003637858,0.002253631,0.0008718516,0.002144043,0.000626909,0.0004195817,0.002245538],"category_scores_gemma":[0.003016129,0.000197254,0.0004723503,0.001069864,0.00283992,0.002968149,0.001051486,0.00103768,0.0003870972],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001780635,"about_ca_system_score_gemma":0.0006787779,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007112063,"about_ca_topic_score_gemma":0.0006247825,"domain_scores_codex":[0.9994147,0.000103954,0.00003863599,0.0001131031,0.0002267707,0.0001029319],"domain_scores_gemma":[0.9982157,0.0004264009,0.0005625127,0.0001196209,0.0002475385,0.000428276],"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":[0.00001611319,0.00001185674,0.0007689447,0.00001140097,0.000003018693,0.00003001177,0.0001328373,0.0006552857,0.001347184,0.99462,0.0002188615,0.002184507],"study_design_scores_gemma":[0.00001540375,0.00005184497,0.00308744,0.00001696133,0.000005922578,0.0002094797,0.0001913323,0.01598156,0.002358934,0.9754115,0.002626932,0.0000426612],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8609887,0.0006932957,0.1111242,0.0005301082,0.0001078395,0.00003793221,0.0003014583,0.0001725999,0.02604372],"genre_scores_gemma":[0.9874608,0.0002485546,0.007415252,0.00007792379,0.0001932572,0.00004135447,0.0001497925,0.00002733348,0.004385672],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002253631,"threshold_uncertainty_score":0.01291943,"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."}}