Fields of Character Values for Finite Special Unitary Groups

TL;DR

This paper extends the description of the fields of character values from special linear groups to special unitary groups, providing a broader understanding of character fields in finite groups of Lie type.

Contribution

It generalizes Turull's results on $SL_n(q)$ to the case of $SU_n(q)$, expanding the knowledge of character value fields for finite groups.

Findings

Fields of character values for $SU_n(q)$ are characterized.

Extension of Turull's parametrization to $SU_n(q)$.

Provides a framework for understanding character fields in unitary groups.

Abstract

Turull has described the fields of values for characters of $SL_n(q)$ in terms of the parametrization of the characters of $GL_n(q)$. In this article, we extend these results to the case of $SU_n(q)$.