Regular irreducible representations of classical groups over finite quotient rings

Koichi Takase

Vol. 311 (2021), No. 1, 221–256

DOI: 10.2140/pjm.2021.311.221

Abstract

A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a nondyadic nonarchimedean local field is presented. The parametrization is given by means of (a subset of) the character group of the centralizer of a representative of the regular adjoint orbit. Our method is based upon Weil representations over finite fields. More explicit parametrization in terms of tamely ramified extensions of the base field is given for the general linear group, the special linear group, the symplectic group and the orthogonal group.

Keywords

Weil representation, reductive group, finite ring

Mathematical Subject Classification

Primary: 20C15

Secondary: 20C33

Milestones

Received: 18 April 2019

Revised: 2 September 2020

Accepted: 23 October 2020

Published: 17 March 2021