{
  "id": "1907.10089",
  "version": "v1",
  "published": "2019-07-19T18:42:54.000Z",
  "updated": "2019-07-19T18:42:54.000Z",
  "title": "Representation ring of Levi subgroups versus cohomology ring of flag varieties II",
  "authors": [
    "Shrawan Kumar",
    "Sean Rogers"
  ],
  "comment": "19 pages. arXiv admin note: text overlap with arXiv:1508.06826",
  "categories": [
    "math.RT",
    "math.AT",
    "math.GR"
  ],
  "abstract": "For any reductive group G and a parabolic subgroup P with its Levi subgroup L, the first author in [Ku2] introduced a ring homomorphism $ \\xi^P_\\lambda: Rep^\\mathbb{C}_{\\lambda-poly}(L) \\to H^*(G/P, \\mathbb{C})$, where $ Rep^\\mathbb{C}_{\\lambda-poly}(L)$ is a certain subring of the complexified representation ring of L (depending upon the choice of an irreducible representation $V(\\lambda)$ of G with highest weight $\\lambda$). In this paper we study this homomorphism for G=Sp(2n) and its maximal parabolic subgroups $P_{n-k}$ for any $1\\leq k\\leq n$ (with the choice of $V(\\lambda) $ to be the defining representation $V(\\omega_1) $ in $\\mathbb{C}^{2n}$). Thus, we obtain a $\\mathbb{C}$-algebra homomorphism $ \\xi_{n,k}: Rep^\\mathbb{C}_{\\omega_1-poly}(Sp(2k)) \\to H^*(IG(n-k, 2n), \\mathbb{C})$. Our main result asserts that $ \\xi_{n,k}$ is injective when n tends to $\\infty$ keeping k fixed. Similar results are obtained for the odd orthogonal groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-19T18:42:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "14N15",
      "14L35",
      "14M15"
    ],
    "keywords": [
      "levi subgroup",
      "representation ring",
      "flag varieties",
      "cohomology ring",
      "homomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}