{"id":"W2964747572","doi":"10.1007/s00029-021-00654-1","title":"Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials","year":2021,"lang":"en","type":"preprint","venue":"Selecta Mathematica","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Ottawa; National Science Foundation","keywords":"Mathematics; Weyl group; Pure mathematics; Macdonald polynomials; Hecke operator; Algebra over a field; Koornwinder polynomials; Hecke algebra; Representation theory; Action (physics); Quotient; Affine transformation; Group (periodic table); Orthogonal polynomials; Modular form; Difference polynomials","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003781359,0.0002968294,0.0003021144,0.0008246224,0.0008294414,0.001302584,0.0004837755,0.0005590671,0.003142967],"category_scores_gemma":[0.0008092695,0.0001865192,0.0005693058,0.0005089045,0.002278469,0.002060711,0.001105293,0.001074793,0.0004833922],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000771909,"about_ca_system_score_gemma":0.0003396551,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004690531,"about_ca_topic_score_gemma":0.0003766594,"domain_scores_codex":[0.9997209,0.00006026371,0.0000113151,0.00004866491,0.00007771204,0.00008115805],"domain_scores_gemma":[0.9997427,0.00004130086,0.00005521176,0.00007444995,0.00002544807,0.00006089388],"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":[0.00002335541,0.00002312173,0.0002208035,0.00001055739,0.000003195094,0.00009121663,0.0002280998,0.001284691,0.002383314,0.992775,0.0003114022,0.00264532],"study_design_scores_gemma":[0.00003137828,0.00008136113,0.0006018651,0.00001602326,0.00001039663,0.0002599968,0.0002521747,0.01444714,0.005830882,0.9749966,0.003446691,0.00002555499],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9034056,0.0002948016,0.06084266,0.0007622695,0.00008252929,0.00003619466,0.0001003171,0.0003156285,0.03416015],"genre_scores_gemma":[0.9893885,0.0001168024,0.005300829,0.00006312044,0.00004339768,0.0000180832,0.00003883856,0.00003234137,0.004998007],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003142967,"threshold_uncertainty_score":0.0105142,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05563645095581866,"score_gpt":0.3487482903601124,"score_spread":0.2931118394042938,"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."}}