{ "id": "2407.06865", "version": "v1", "published": "2024-07-09T13:53:08.000Z", "updated": "2024-07-09T13:53:08.000Z", "title": "Affine $\\imath$quantum groups and Steinberg varieties of type C", "authors": [ "Changjian Su", "Weiqiang Wang" ], "comment": "47 pages. Comments are welcome", "categories": [ "math.RT", "math.QA" ], "abstract": "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.", "revisions": [ { "version": "v1", "updated": "2024-07-09T13:53:08.000Z" } ], "analyses": { "keywords": [ "quantum group", "composition multiplicity formula", "finite-dimensional standard modules", "drinfeld type presentation", "nontrivial serre relations" ], "note": { "typesetting": "TeX", "pages": 47, "language": "en", "license": "arXiv", "status": "editable" } } }