{
  "id": "1605.08545",
  "version": "v1",
  "published": "2016-05-27T08:55:07.000Z",
  "updated": "2016-05-27T08:55:07.000Z",
  "title": "On certain representations of the general linear group over a non-archimedean local field",
  "authors": [
    "Erez Lapid",
    "Alberto Minguez"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\pi$ be an irreducible, complex, smooth representation of $GL_n$ over a local non-archimedean (skew) field. We give a simple combinatorial sufficient condition for the irreducibility of the parabolic induction of $\\pi\\otimes\\pi$ to $GL_{2n}$. The latter irreducibility property is the $p$-adic analogue of a special case of the notion of \"real representations\" introduced by Leclerc and studied recently by Kang--Kashiwara--Kim--Oh (in the context of KLR algebras). Our sufficient condition is closely related to singularities of Schubert varieties of type $A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-27T08:55:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general linear group",
      "non-archimedean local field",
      "simple combinatorial sufficient condition",
      "real representations",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}