# Computation of Irreducible Characters of GL(5,q)

## TL;DR

This paper computes the irreducible characters of the five-dimensional general linear group over a finite field, extending the understanding of its representation theory using Green's techniques.

## Contribution

It provides the explicit determination of all irreducible characters of GL(5,q), a significant advancement in the representation theory of finite groups.

## Key findings

- Complete set of irreducible characters for GL(5,q) determined
- Methodology based on Green's techniques applied to higher dimensions
- Enhances understanding of the structure of linear groups over finite fields

## Abstract

In this paper we determine the ordinary irreducible characters of the five-dimensional full linear group over a Galois field of q elements. We use the techniques developed by J. A. Green.