{
  "id": "2205.15313",
  "version": "v1",
  "published": "2022-05-29T16:14:41.000Z",
  "updated": "2022-05-29T16:14:41.000Z",
  "title": "Shalika models for general linear groups",
  "authors": [
    "Itay Naor"
  ],
  "comment": "24 pages. M.Sc. thesis completed at Weizmann Institute of Science under the guidance of Prof. Dmitry Gourevitch",
  "categories": [
    "math.RT"
  ],
  "abstract": "We define a generalization of Shalika models for $GL_{n+m}(F)$ and prove that they are multiplicity-free, where $F$ is either a non-Archimedean local field or a finite field and $n,m$ are any natural numbers. In particular, we give new proof for the case of $n=m$. We also show that the Bernstein-Zelevinsky product of an irreducible representation of $GL_n(F)$ and the trivial representation of $GL_m(F)$ is multiplicity-free. We relate the two results by a conjecture about twisted parabolic induction of Gelfand pairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-29T16:14:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "46F10",
      "22E50",
      "20C33",
      "22E50"
    ],
    "keywords": [
      "general linear groups",
      "shalika models",
      "non-archimedean local field",
      "multiplicity-free",
      "twisted parabolic induction"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}