{"id":"W2351714999","doi":"","title":"PAIRING PROBLEM OF GENERATORS IN AFFINE KAC-MOODY LIE ALGEBRAS","year":2005,"lang":"en","type":"article","venue":"Chinese Annals of Mathematics,series A","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Affine Lie algebra; Affine transformation; Lie algebra; Pairing; Kac–Moody algebra; Pure mathematics; Lie conformal algebra; Algebra over a field; Type (biology); Affine representation; Adjoint representation of a Lie algebra; Current algebra; Physics","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":[0.002027273,0.0005443364,0.001193794,0.001331361,0.003849186,0.003984196,0.001040614,0.003089895,0.009960624],"category_scores_gemma":[0.004457588,0.00067329,0.001078235,0.001066569,0.003093785,0.01029243,0.003491402,0.00285692,0.001912434],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009098094,"about_ca_system_score_gemma":0.0006250068,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002056498,"about_ca_topic_score_gemma":0.0001321295,"domain_scores_codex":[0.9983432,0.000809597,0.0001137663,0.0002651346,0.0002371989,0.0002310865],"domain_scores_gemma":[0.9986993,0.0005580341,0.0001835197,0.0001417498,0.0001705775,0.0002468391],"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":[0.00003262353,0.00002098984,0.0001819726,0.00002869067,0.000003502048,0.0001580922,0.0002294366,0.0004423499,0.0002713202,0.9955362,0.0006417077,0.002453122],"study_design_scores_gemma":[0.00002220325,0.00003620123,0.0000789343,0.00001595085,0.000004508464,0.0001951027,0.0002818952,0.002491265,0.0006237864,0.9935768,0.002662895,0.000010411],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5497477,0.001740056,0.3105155,0.005970545,0.0008928958,0.0002377344,0.0004729619,0.0003363654,0.1300862],"genre_scores_gemma":[0.948085,0.00054722,0.03136336,0.0004346935,0.0003949201,0.0001673248,0.0003676214,0.00008899096,0.01855083],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009960624,"threshold_uncertainty_score":0.03332162,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04733282034064226,"score_gpt":0.322640726093299,"score_spread":0.2753079057526568,"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."}}