{
  "id": "2405.20007",
  "version": "v1",
  "published": "2024-05-30T12:44:34.000Z",
  "updated": "2024-05-30T12:44:34.000Z",
  "title": "On the restriction of some irreducible mod-$p$ representations of $\\text{GL}_2(\\mathbb{F}_q)$ to $\\text{GL}_2(\\mathbb{F}_p)$",
  "authors": [
    "Shubhanshi Gupta"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "For a prime $p,$ let $\\mathbb{F}_q$ be a finite extension of $\\mathbb{F}_p$ and $\\mathcal{G}=\\text{GL}_2(\\mathbb{F}_q).$ Then the irreducible representations of $\\mathcal{G}$ are classified as twists of Sym$^{\\vec{r}}(\\overline{\\mathbb F}_{p^2}).$ The restriction of irreducibles of $\\mathcal{G}$ to its subgroup $G=\\text{GL}_2(\\mathbb{F}_p)$ is same as investigating the behavior of the tensor product of irreducible representations of $G.$ In this paper, we study the restriction of some of these representations of $\\mathcal{G}$ to $G,$ for $2$ and $3$ degree extensions of $\\mathbb{F}_p.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-30T12:44:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "restriction",
      "irreducible representations",
      "degree extensions",
      "finite extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}