Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields

  • Mohammad Bardestani

    University of Ottawa, Canada
  • Camelia Karimianpour

    University of Ottawa, Canada
  • Keivan Mallahi-Karai

    Jacobs-Universität Bremen, Germany
  • Hadi Salmasian

    University of Ottawa, Canada

Abstract

Let be a non-Archimedean local field with the ring of integers and the prime ideal and let be the adjoint Chevalley group. Let denote the smallest possible dimension of a faithful representation of . Using the Stone–von Neumann theorem, we determine a lower bound for which is asymptotically the same as the results of Landazuri, Seitz and Zalesskii for split Chevalley groups over . Our result yields a conceptual explanation of the exponents that appear in the aforementioned results.

Cite this article

Mohammad Bardestani, Camelia Karimianpour, Keivan Mallahi-Karai, Hadi Salmasian, Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields. Groups Geom. Dyn. 11 (2017), no. 1, pp. 57–74

DOI 10.4171/GGD/387