{
  "id": "math/0512187",
  "version": "v2",
  "published": "2005-12-09T07:57:45.000Z",
  "updated": "2007-06-12T12:04:45.000Z",
  "title": "Equivariant K-theory of compactifications of algebraic groups",
  "authors": [
    "V. Uma"
  ],
  "comment": "41 pages, To appear in Transformation Groups",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "In this article we describe the $G\\times G$-equivariant $K$-ring of $X$, where $X$ is a regular compactification of a connected complex reductive algebraic group $G$. Furthermore, in the case when $G$ is a semisimple group of adjoint type, and $X$ its wonderful compactification, we describe its ordinary $K$-ring $K(X)$. More precisely, we prove that $K(X)$ is a free module over $K(G/B)$ of rank the cardinality of the Weyl group. We further give an explicit basis of $K(X)$ over $K(G/B)$, and also determine the structure constants with respect to this basis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-06-12T12:04:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19L47",
      "14M17",
      "14L30"
    ],
    "keywords": [
      "equivariant k-theory",
      "connected complex reductive algebraic group",
      "regular compactification",
      "semisimple group",
      "explicit basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12187U"
    }
  }
}