{
  "id": "1510.07352",
  "version": "v1",
  "published": "2015-10-26T02:29:18.000Z",
  "updated": "2015-10-26T02:29:18.000Z",
  "title": "Quantum Hamiltonian reduction of W-algebras and category O",
  "authors": [
    "Stephen Morgan"
  ],
  "comment": "22 pages. This is the journal version of my PhD thesis (arXiv:1502.07025 [math.RT]) with extended results",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We define a quantum version of Hamiltonian reduction by stages, producing a construction in type A for a quantum Hamiltonian reduction from the W-algebra $U(\\mathfrak{g},e_1)$ to an algebra conjecturally isomorphic to $U(\\mathfrak{g},e_2)$, whenever $e_2 \\ge e_1$ in the dominance ordering. This isomorphism is shown to hold whenever $e_1$ is subregular, and in $\\mathfrak{sl}_n$ for all $n \\le 4$. We next define embeddings of various categories $\\mathcal{O}$ for the W-algebras associated to $e_1$ and $e_2$, amongst them the embeddings $\\mathcal{O}(e_2,\\mathfrak{p}) \\hookrightarrow \\mathcal{O}(e_1,\\mathfrak{p})$, where $\\mathfrak{p}$ is a parabolic subalgebra containing both $e_1$ and $e_2$ in its Levi subalgebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-26T02:29:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum hamiltonian reduction",
      "quantum version",
      "parabolic subalgebra",
      "define embeddings",
      "levi subalgebra"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007352M"
    }
  }
}