{
  "id": "1105.3802",
  "version": "v2",
  "published": "2011-05-19T07:19:22.000Z",
  "updated": "2012-02-14T11:11:28.000Z",
  "title": "Extensions of tempered representations",
  "authors": [
    "Eric Opdam",
    "Maarten Solleveld"
  ],
  "comment": "This paper grew out of \"A formula of Arthur and affine Hecke algebras\" (arXiv:1011.0679). In the second version some minor points were improved",
  "journal": "Geometric And Functional Analysis 23 (2013), 664-714",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\pi, \\pi'$ be irreducible tempered representations of an affine Hecke algebra H with positive parameters. We compute the higher extension groups $Ext_H^n (\\pi,\\pi')$ explicitly in terms of the representations of analytic R-groups corresponding to $\\pi$ and $\\pi'$. The result has immediate applications to the computation of the Euler-Poincar\\'e pairing $EP(\\pi,\\pi')$, the alternating sum of the dimensions of the Ext-groups. The resulting formula for $EP(\\pi,\\pi')$ is equal to Arthur's formula for the elliptic pairing of tempered characters in the setting of reductive p-adic groups. Our proof applies equally well to affine Hecke algebras and to reductive groups over non-archimedean local fields of arbitrary characteristic. This sheds new light on the formula of Arthur and gives a new proof of Kazhdan's orthogonality conjecture for the Euler-Poincar\\'e pairing of admissible characters.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-14T11:11:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "22E35",
      "22E50"
    ],
    "keywords": [
      "tempered representations",
      "affine hecke algebra",
      "kazhdans orthogonality conjecture",
      "higher extension groups",
      "non-archimedean local fields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.3802O"
    }
  }
}