On Jordan Decomposition of Characters for SU(n,q)

TL;DR

This paper extends the Jordan decomposition of characters to finite special unitary groups, adapting existing methods for special linear groups, and ensures compatibility with Lusztig's twisted induction.

Contribution

It provides a new Jordan decomposition of characters for SU(n,q), adapting Bonnafé's methods for the special linear case to the unitary case.

Findings

Established a Jordan decomposition for SU(n,q) characters.

Demonstrated compatibility with Lusztig's twisted induction.

Extended parametrization techniques to unitary groups.

Abstract

As shown by Bonnaf\'e, a step in proving a Jordan decomposition of characters of finite special linear groups is the parametrization of unipotent characters of centralizers of semi-simple elements in projective linear groups. We show the same kind of result in the case of finite special unitary groups. The proof leads to a mild adaptation of Bonnaf\'e's methods expounded in [B99]. The outcome is a Jordan decomposition of characters compatible with Lusztig's twisted induction.