{
  "id": "1409.4670",
  "version": "v1",
  "published": "2014-09-16T15:10:28.000Z",
  "updated": "2014-09-16T15:10:28.000Z",
  "title": "Class polynomials for some affine Hecke algebras",
  "authors": [
    "Zhongwei Yang"
  ],
  "comment": "40 pages, comments are welcome. arXiv admin note: text overlap with arXiv:1201.4901 by other authors",
  "categories": [
    "math.RT",
    "math.AG",
    "math.NT"
  ],
  "abstract": "Class polynomials attached to affine Hecke algebras were first introduced by X.~He in \\cite{He1}. They play an important role in the study of affine Deligne-Lusztig varieties. Motivated by \\cite{He2}, we compute the class polynomials attached to an affine Hecke algebra of type (twisted) $\\widetilde{A}_2$. Using these class polynomials we prove a conjecture of G\\\"{o}rtz-Haines-Kottwitz-Reuman for the general linear group, unitary group and division algebra of semisimple rank 2. Furthermore, we discuss some interesting patterns on affine Deligne-Lusztig varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-16T15:10:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "11Gxx",
      "14Lxx"
    ],
    "keywords": [
      "affine hecke algebra",
      "affine deligne-lusztig varieties",
      "class polynomials",
      "general linear group",
      "semisimple rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.4670Y"
    }
  }
}