{
  "id": "2411.18273",
  "version": "v1",
  "published": "2024-11-27T12:07:41.000Z",
  "updated": "2024-11-27T12:07:41.000Z",
  "title": "Geometric construction of Schur algebras",
  "authors": [
    "Li Luo",
    "Zheming Xu",
    "Yang Yang"
  ],
  "comment": "50 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We provide the geometric construction of a series of generalized Schur algebras of any type via Borel-Moore homologies and equivariant K-groups of generalized Steinberg varieties. As applications, we obtain a Schur algebra analogue of the local geometric Langlands correspondence of any finite type, provide an equivariant K-theoretic realization of quasi-split $\\imath$quantum groups of affine type AIII, and establish a geometric Howe duality for affine ($\\imath$-)quantum groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-27T12:07:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric construction",
      "quantum groups",
      "local geometric langlands correspondence",
      "equivariant k-theoretic realization",
      "geometric howe duality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}