2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127418When n is odd, consider the finite general linear and unitary groups of rank n, extended by the inverse transpose automorphism. There are elements in the extended groups which square to a regular unipotent element, and we evaluate the values of irreducible characters of the extended groups on these elements. Several intermediate results on real conjugacy classes and real-valued characters of these groups are obtained along the way.27 pagesRepresentation TheoryGroup Theory20G05; 20G40text