{
  "id": "2006.05271",
  "version": "v1",
  "published": "2020-06-05T19:09:42.000Z",
  "updated": "2020-06-05T19:09:42.000Z",
  "title": "Tensor product decompositions for cohomologies of Bott-Samelson varieties",
  "authors": [
    "Vladimir Shchigolev"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2006.00551",
  "categories": [
    "math.RT",
    "math.AG",
    "math.AT"
  ],
  "abstract": "Let $T$ be a maximal torus of a semisimple complex algebraic group, $\\mathrm{BS}(s)$ be the Bott-Samelson variety for a sequence of simple reflections $s$ and $\\mathrm{BS}(s)^T$ be the set of $T$-fixed points of $\\mathrm{BS}(s)$. We prove the tensor product decompositions for the image of the restriction $H^\\bullet_T(\\mathrm{BS}(s),k)\\to H_T^\\bullet(X,k)$, where $X\\subset\\mathrm{BS}(s)^T$ is defined by some special not overlapping equations $\\gamma_i\\gamma_{i+1}\\cdots\\gamma_j=w_{i,j}$ with right-hand sides belonging to the Weyl group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-05T19:09:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N91"
    ],
    "keywords": [
      "tensor product decompositions",
      "bott-samelson variety",
      "semisimple complex algebraic group",
      "cohomologies",
      "right-hand sides"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}