{"paper":{"title":"Affine $\\imath$quantum groups and Steinberg varieties of type C","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Changjian Su, Weiqiang Wang","submitted_at":"2024-07-09T13:53:08Z","abstract_excerpt":"We provide a geometric realization of the quasi-split affine $\\imath$quantum group of type AIII$_{2n-1}^{(\\tau)}$ in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine $\\imath$quantum group which admits very nontrivial Serre relations. We then construct \\`a la Springer a family of finite-dimensional standard modules and irreducible modules of this $\\imath$quantum group, and provide a composition multiplicity formula of the standard modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06865","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.06865/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}