{
  "id": "1912.04997",
  "version": "v1",
  "published": "2019-12-10T21:54:27.000Z",
  "updated": "2019-12-10T21:54:27.000Z",
  "title": "$\\mathbb{P}\\mathfrak{gl}_{2}$ is Multiplicity-Free as a $PGL_{2} \\times PGL_{2}$-Variety",
  "authors": [
    "Dmitry Gourevitch",
    "Shai Keidar"
  ],
  "comment": "MSc thesis completed at Weizmann Institute of Science under the guidance of Prof. Dmitry Gourevitch",
  "categories": [
    "math.RT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "Let $F$ be a non-Archimedean local field. Let $G$ be an algebraic group over $F$. A $G$-variety $X$ defined over $F$ is said to be multiplicity-free if for any admissible irreducible representation $\\pi$ of $G(F)$ the following takes place: $\\dim Hom_{G(F)}(\\mathcal{S}(X(F)), \\pi) \\le 1$ where $\\mathcal{S}(X(F))$ is the space of Schwartz functions on $X(F)$. In this thesis we prove that $\\mathbb{P}\\mathfrak{gl}_{2}(F)$ is multiplicity-free as a $PGL_{2}(F)\\times PGL_{2}(F)$-variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-10T21:54:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicity-free",
      "non-archimedean local field",
      "algebraic group",
      "schwartz functions"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}