{
  "id": "0903.3744",
  "version": "v1",
  "published": "2009-03-23T17:33:22.000Z",
  "updated": "2009-03-23T17:33:22.000Z",
  "title": "MV-Polytopes via affine buildings",
  "authors": [
    "Michael Ehrig"
  ],
  "comment": "34 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We give a construction of MV-polytopes of a complex semisimple algebraic group G in terms of the geometry of the Bott-Samelson variety and the affine building. This is done by using the construction of dense subsets of MV-cycles by Gaussent and Littelmann. They used LS-gallery to define subsets in the Bott-Samelson variety that map to subsets of the affine Grassmannian, whose closure are MV-cycles. Since points in the Bott-Samelson variety correspond to galleries in the affine building one can look at the image of a point in such a special subset under all retractions at infinity. We prove that these images can be used to construct the corresponding MV-polytope in an explicit way, by using the GGMS strata. Furthermore we give a combinatorial construction for these images by using the crystal structure of LS-galleries and the action of the ordinary Weyl group on the coweight lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-23T17:33:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "14M15"
    ],
    "keywords": [
      "affine building",
      "mv-polytope",
      "complex semisimple algebraic group",
      "ordinary weyl group",
      "bott-samelson variety correspond"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.3744E"
    }
  }
}