On Representations of Classical Groups over Finite Local Rings of Length Two

TL;DR

This paper investigates the complex irreducible representations of classical groups over finite local rings of length two, establishing a canonical correspondence that preserves dimensions across these groups.

Contribution

It extends previous work on general linear groups to classical groups, providing a unified framework for their irreducible representations over specific local rings.

Findings

Constructed a canonical correspondence between irreducible representations of classical groups.

Preserved dimensions in the correspondence across different classical groups.

Extended the representation theory framework from general linear to classical groups.

Abstract

We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of all such groups that preserves dimensions. The case for general linear groups has already been proved by author.