{
  "id": "2501.04301",
  "version": "v1",
  "published": "2025-01-08T06:20:33.000Z",
  "updated": "2025-01-08T06:20:33.000Z",
  "title": "On extensions of principal series representations",
  "authors": [
    "Gautam H. Borisagar",
    "Asfak Soneji"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We compute $\\mathrm{Ext}^{1}_B(\\chi_1,\\chi_2)$ between two characters $\\chi_1,\\chi_2$ of a Borel subgroup $B$ of a split reductive group $G$ over a finite field $\\mathbb{F}_q,$ and make an application to the calculation of $\\mathrm{Ext}^1_G(\\pi_1,\\pi_2)$ between principal series representations $\\pi_1,\\pi_2$ of $G(\\mathbb{F}_q).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-08T06:20:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal series representations",
      "extensions",
      "borel subgroup",
      "split reductive group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}