Subregular characters of the unitriangular group over a finite field

TL;DR

This paper provides an explicit formula for subregular characters of the unitriangular group over a finite field, focusing on irreducible characters of submaximal degree in large characteristic.

Contribution

It introduces a new explicit formula for subregular characters of the unitriangular group over finite fields, advancing understanding of their representation theory.

Findings

Derived an explicit formula for subregular characters

Characterized irreducible characters of submaximal degree

Applicable to finite fields of sufficiently large characteristic

Abstract

We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.