{
  "abstract": "Let $\\mathbf{G}$ be a connected unramified quasi-split reductive group defined over a nonarchimedean local field $F$. This paper concerns the Iwahori Whittaker functions attached to the unramified principal series of $\\mathbf{G}(F)$. We introduce Demazure-Whittaker operators and show that in the non-split case they generate a Hecke algebra with unequal parameters that are determined by $\\mathbf{G}$. We then connect these operators to the Whittaker functions, establishing formulas for calculating all values for a basis of Iwahori Whittaker functions and giving a new proof of the Casselman-Shalika formula for the spherical Whittaker function. In doing so we build on the work for split groups of Brubaker, Bump and Licata; the new feature here is the appearance of a Hecke algebra with unequal parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37614",
  "author_total": 3,
  "authors": [
    {
      "name": "Solomon Friedberg"
    },
    {
      "name": "Claire Frechette"
    },
    {
      "name": "Henrik P. A. Gustafsson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0x1qwc91x1hvw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37614",
  "fulltext_url": null,
  "id": "0x1qwc91x1hvw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37614",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7224083766",
  "pdf_url": "https://arxiv.org/pdf/2610.37614",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0x1qwc91x1hvw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37614",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37614"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Iwahori Whittaker functions for unramified quasi-split groups",
  "title_text": "Iwahori Whittaker functions for unramified quasi-split groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/0x1qwc91x1hvw",
  "venue": "arXiv",
  "versions": []
}