{
  "id": "1809.09394",
  "version": "v1",
  "published": "2018-09-25T10:12:01.000Z",
  "updated": "2018-09-25T10:12:01.000Z",
  "title": "Large annihilator category O for sl_{\\infty}, o_{\\infty}, sp_{\\infty}",
  "authors": [
    "Ivan Penkov",
    "Vera Serganova"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct a new analogue of the BGG category $\\mathcal O$ for the infinite-dimensional Lie algebras $\\fg=\\mathfrak{sl}(\\infty),\\mathfrak{o}(\\infty), \\mathfrak{sp}(\\infty)$. A main difference with the categories studied in \\cite{Nam} and \\cite{CP} is that all objects of our category satisfy the large annihilator condition introduced in \\cite{DPS}. Despite the fact that the splitting Borel subalgebras $\\fb$ of $\\fg$ are not conjugate, one can eliminate the dependency on the choice of $\\fb$ and introduce a universal highest weight category $\\mathcal {OLA}$ of $\\fg$-modules, the letters $\\mathcal{LA}$ coming from \"large annihilator\". The subcategory of integrable objects in $\\mathcal {OLA}$ is precisely the category $\\mathbb T_{\\fg}$ studied in \\cite{DPS}. We investigate the structure of $\\mathcal {OLA}$, and in particular compute the multiplicities of simple objects in standard objects and the multiplicities of standard objects in indecomposable injectives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-25T10:12:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "16S37",
      "17B55"
    ],
    "keywords": [
      "large annihilator category",
      "standard objects",
      "universal highest weight category",
      "large annihilator condition",
      "infinite-dimensional lie algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}