A question of Katz and Tiep on representations of finite general unitary groups

Abstract

Katz and Tiep proved a characterization of the total Weil character of finite special unitary groups for any integer and any prime power q other than in terms of the character values and irreducible constituents. They asked whether a similar characterization can be done for finite general unitary groups In this article, we prove that such characterization for can be done up to endomorphisms and tensoring by real linear characters.