{"id":"W3155975329","doi":"10.1093/imrn/rnab049","title":"Left Demazure–Lusztig Operators on Equivariant (Quantum) Cohomology and K-Theory","year":2021,"lang":"en","type":"article","venue":"International Mathematics Research Notices","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Japan Society for the Promotion of Science","keywords":"Mathematics; Equivariant map; Generalized flag variety; Flag (linear algebra); Equivariant cohomology; Pure mathematics; Schubert calculus; Quantum cohomology; Cohomology; Algebra over a field; Lie group; Grassmannian","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.002018492,0.0002350797,0.0003723264,0.0002471895,0.0002694359,0.0003252536,0.0006303001,0.0001846204,0.00124302],"category_scores_gemma":[0.006151442,0.0001946826,0.00009090597,0.0001725416,0.0002896528,0.0001724722,0.0005559583,0.0005748706,0.00009196705],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001198808,"about_ca_system_score_gemma":0.0001970911,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001263582,"about_ca_topic_score_gemma":0.00001937282,"domain_scores_codex":[0.9968105,0.0004221585,0.0005034049,0.0004872657,0.001295355,0.0004813319],"domain_scores_gemma":[0.993363,0.005014258,0.0001399283,0.0005046184,0.0007978707,0.0001803843],"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":[0.00005030457,0.0002776516,0.00008099199,0.0001305543,0.0002031238,0.0001381457,0.001122388,0.00001915804,0.0005745291,0.9961674,0.0009054885,0.0003302389],"study_design_scores_gemma":[0.0005329364,0.0001216504,0.0001115193,0.0001798264,0.00002539645,0.0001065521,0.0009011551,0.003292754,0.003410989,0.9897681,0.00134547,0.000203615],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9673505,0.0002918424,0.002889377,0.002942055,0.001525738,0.0003839799,0.00002498337,0.00009034682,0.02450115],"genre_scores_gemma":[0.9907615,0.00008329829,0.006210066,0.000195388,0.0003417231,0.00002819209,0.000009343119,0.00005101832,0.002319529],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02341091,"threshold_uncertainty_score":0.99967,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1337465505609688,"score_gpt":0.4287045451670813,"score_spread":0.2949579946061125,"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."}}