{"id":"W2022171604","doi":"10.1063/1.3087425","title":"Automorphisms of the Heisenberg–Weyl algebra and d-orthogonal polynomials","year":2009,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":27,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"Université de Montréal; Centre de Recherches Mathématiques","keywords":"Orthogonal polynomials; Wilson polynomials; Mathematics; Discrete orthogonal polynomials; Classical orthogonal polynomials; Weyl algebra; Hahn polynomials; Algebra over a field; Automorphism; Macdonald polynomials; Hermite polynomials; Pure mathematics; Difference polynomials; Heisenberg group; Gegenbauer 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":[0.0005351321,0.0004297141,0.0003472515,0.0009828855,0.0009031963,0.001487854,0.0004629161,0.0005193417,0.003009641],"category_scores_gemma":[0.001530274,0.0002201275,0.0007874434,0.0007504695,0.002425559,0.002246035,0.001469928,0.00115116,0.0006148319],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007148454,"about_ca_system_score_gemma":0.0005583272,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001016657,"about_ca_topic_score_gemma":0.0005407517,"domain_scores_codex":[0.9995849,0.00008278766,0.00002540053,0.00007471978,0.0001086469,0.0001236087],"domain_scores_gemma":[0.9993112,0.0001556698,0.0001925864,0.0001401514,0.00009771874,0.0001026082],"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":[0.0000116183,0.00001318833,0.0001019563,0.000008786008,0.000002300088,0.00005875972,0.0001055515,0.0007265517,0.001346169,0.994764,0.0002248734,0.002636219],"study_design_scores_gemma":[0.00001117017,0.00002492947,0.000215917,0.000005865375,0.000003445072,0.0001536136,0.00006875172,0.006892876,0.001773428,0.9882252,0.002606387,0.00001831379],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.691216,0.0008103703,0.209956,0.0009652236,0.0004582722,0.00008649588,0.0002101342,0.0001683588,0.09612904],"genre_scores_gemma":[0.9705146,0.0004836204,0.01629402,0.000199827,0.0002420117,0.00004617196,0.0001045269,0.00004375594,0.01207144],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003009641,"threshold_uncertainty_score":0.0100683,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009976640299249702,"score_gpt":0.2495317390661727,"score_spread":0.239555098766923,"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."}}