{
  "annotation_id": "632b5cab-98f2-49aa-963b-d54b11b72567",
  "date_created": "2026-02-17T05:53:26.423000Z",
  "date_modified": "2026-02-17T05:53:26.423000Z",
  "file_hash": "6baf8fcefd12e56b020a572e11e7dba132316543b41e37f566bd1b6d38d6ee7a",
  "private": false,
  "record": {
    "abstract": "Let $\\mathfrak{o}$ be the ring of integers of a non-archimedean local field with residue field of odd characteristic, $\\mathfrak{p}$ be its maximal ideal and let $\\mathfrak{o}_\\ell = \\mathfrak{o}/\\mathfrak{p}^\\ell$ for $\\ell\\ge 2$. In this article, we study real-valued characters and real representations of the finite groups $\\mathrm{GL}_2(\\mathfrak{o}_\\ell)$ and $\\mathrm{GU}_2(\\mathfrak{o}_\\ell)$. We give a complete classification of real and strongly real classes of these groups and characterize the real-valued irreducible complex characters. We prove that every real-valued irreducible complex character of $\\mathrm{GL}_2(\\mathfrak{o}_\\ell)$ is afforded by a representation over $\\mathbb{R}$. In contrast, we show that $\\mathrm{GU}_2(\\mathfrak{o}_\\ell)$ admits real-valued irreducible characters that are not realizable over $\\mathbb{R}$. These results extend the parallel known phenomena for the finite groups $\\mathrm{GL}_n(\\mathbb{F}_q)$ and $\\mathrm{GU}_n(\\mathbb{F}_q)$.",
    "arxiv_id": "2601.10670",
    "authors": [
      "Archita Gupta",
      "Tejbir Lohan",
      "Pooja Singla"
    ],
    "categories": [
      "math.RT",
      "math.GR",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Real characters and real classes of $\\mathrm{GL}_2$ and $\\mathrm{GU}_2$ over discrete valuation rings",
    "url": "https://arxiv.org/abs/2601.10670",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ab7f8e9c-26fb-4cf9-aaa2-20e9c3ab2e18",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}