{
  "id": "2412.15346",
  "version": "v1",
  "published": "2024-12-19T19:23:14.000Z",
  "updated": "2024-12-19T19:23:14.000Z",
  "title": "Type I Howe Duality over Finite Fields",
  "authors": [
    "Sophie Kriz"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper, we consider higher tensor powers of oscillator representations over finite fields. We find a decomposition of their endomorphism algebras into group algebras of orthogonal groups, giving a new version of Howe duality for a certain range of Type I reductive dual pairs. Specifically, we find that all occurring terms arise from parabolic inductions and the eta correspondence of R. Howe and S. Gurevich. This also leads to a version of Howe duality in a certain category \"interpolating\" the oscillator representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-19T19:23:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "20C33",
      "20G40"
    ],
    "keywords": [
      "howe duality",
      "finite fields",
      "oscillator representations",
      "higher tensor powers",
      "group algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}