Vol. 311, No. 1, 2021

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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.

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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
Authors
Koichi Takase
Department of Mathematics
Miyagi University of Education
Sendai 980-0845
Japan