The generic character table of a Sylow $p$-subgroup of a finite Chevalley group of type $D_4$

TL;DR

This paper constructs the generic character table for a Sylow p-subgroup of a finite Chevalley group of type D4, providing a detailed algebraic description relevant to representation theory.

Contribution

It introduces a method to explicitly construct the generic character table of Sylow p-subgroups in type D4 Chevalley groups, advancing understanding of their representation structure.

Findings

Explicit construction of the generic character table

Detailed algebraic description of Sylow p-subgroup characters

Foundation for further representation-theoretic analysis

Abstract

Let $U$ be a Sylow $p$-subgroup of the finite Chevalley group of type $D_4$ over the field of $q$ elements, where $q$ is a power of a prime $p$. We describe a construction of the generic character table of $U$.