{
  "id": "2209.05536",
  "version": "v1",
  "published": "2022-09-12T18:31:42.000Z",
  "updated": "2022-09-12T18:31:42.000Z",
  "title": "On irreps of a Hecke algebra of a non-reductive group",
  "authors": [
    "David Kazhdan",
    "Alexander Yom Din"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We study irreducible representations of the Hecke algebra of the pair $({\\rm PGL}_2 (F[\\epsilon] / (\\epsilon^2)) , {\\rm PGL}_2 (\\mathcal{O}[\\epsilon] / (\\epsilon^2)))$ where $F$ is a local non-Archimedean field of characteristic different than $2$ and $\\mathcal{O} \\subset F$ is its ring of integers. We expect to apply our analysis to the study of the spectrum of Hecke operators on the space of cuspidal functions on the space of principal ${\\rm PGL}_2$-bundles on curves over rings $\\mathbb{F}_q [\\epsilon] / (\\epsilon^2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-12T18:31:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke algebra",
      "non-reductive group",
      "local non-archimedean field",
      "study irreducible representations",
      "cuspidal functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}