{
  "id": "1111.1868",
  "version": "v1",
  "published": "2011-11-08T10:56:36.000Z",
  "updated": "2011-11-08T10:56:36.000Z",
  "title": "The convolution algebra structure on $K^G(\\mathcal{B} \\times \\mathcal{B})$",
  "authors": [
    "Sian Nie"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT",
    "math.KT"
  ],
  "abstract": "We show that the convolution algebra $K^G(\\mathcal{B} \\times \\mathcal{B})$ is isomorphic to the Based ring of the lowest two-sided cell of the extended affine Weyl group associated to $G$, where $G$ is a connected reductive algebraic group over the field $\\mathbb{C}$ of complex numbers and $\\mathcal{B}$ is the flag variety of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-08T10:56:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convolution algebra structure",
      "extended affine weyl group",
      "lowest two-sided cell",
      "connected reductive algebraic group",
      "complex numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.1868N"
    }
  }
}