{
  "id": "1310.0103",
  "version": "v2",
  "published": "2013-10-01T00:18:55.000Z",
  "updated": "2016-01-27T03:19:13.000Z",
  "title": "A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs",
  "authors": [
    "Huanchen Bao",
    "Weiqiang Wang"
  ],
  "comment": "v2, 92 pages, References and Notes added, introduction modified, i-canonical bases for based U-modules and positivity of i-KL polynomials added, other minor corrections",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satisfy a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. A new theory of canonical bases arising from quantum symmetric pairs is initiated. It is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the BGG category O of the ortho-symplectic Lie superalgebras $\\mathfrak{osp}(2m+1|2n)$. In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-01T00:18:55.000Z",
      "abstract": "We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satisfy a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. We offer a new approach to the Kazhdan-Lusztig theory for the BGG category O for Lie algebras of type B/C by developing a new theory of canonical basis arising from quantum symmetric pairs. This is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the category O of the ortho-symplectic Lie superalgebra osp(2m+1|2n).",
      "comment": "89 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-27T03:19:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum symmetric pair",
      "kazhdan-lusztig theory",
      "coideal subalgebra form",
      "ortho-symplectic lie superalgebras",
      "quantum group satisfy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 92,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0103B"
    }
  }
}