{
  "id": "2405.16872",
  "version": "v1",
  "published": "2024-05-27T06:40:24.000Z",
  "updated": "2024-05-27T06:40:24.000Z",
  "title": "On local character expansions for principal series representations of general linear groups",
  "authors": [
    "Maxim Gurevich"
  ],
  "comment": "to appear in the IMS Lecture Note Series for \"Representations and Characters: Revisiting the Works of Harish-Chandra and Andr\\'e Weil\"",
  "categories": [
    "math.RT"
  ],
  "abstract": "We obtain two explicit formulas for the full local character expansion of any irreducible representation of a p-adic general linear group in principal blocks. The first, generalizing previous work of the author on the Iwahori-spherical case, expresses the expansion in terms of dimensions of degenerate Whittaker models. The second gives a closed expression in terms of values of Kazhdan-Lusztig polynomials of a suitable permutation group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-27T06:40:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal series representations",
      "full local character expansion",
      "p-adic general linear group",
      "degenerate whittaker models",
      "permutation group"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}