Additive Polynomials for Finite Groups of Lie Type

TL;DR

This paper constructs explicit additive polynomials for realizing classical and exceptional finite groups of Lie type as Galois groups over function fields, using a unified approach based on Frobenius modules and algebraic group theory.

Contribution

It provides explicit additive polynomials for all classical and most exceptional finite groups of Lie type as Galois groups over function fields.

Findings

Explicit additive polynomials for classical groups

Realization of most exceptional groups as Galois groups

Unified approach using Frobenius modules and algebraic groups

Abstract

This paper provides a realization of all classical and most exceptional finite groups of Lie type as Galois groups over function fields over F_q and derives explicit additive polynomials for the extensions. Our unified approach is based on results of Matzat which give bounds for Galois groups of Frobenius modules and uses the structure and representation theory of the corresponding connected linear algebraic groups.