2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71730We focus on derangement characters of $GL(n,q)$ which depend solely on the dimension of the space of fixed vectors. This family includes Thoma characters which become asymptotically irreducible as $n\to\infty$. We find explicit decomposition of Thoma characters into irreducibles, construct further derangement characters and seek for extremes in the family of derangement characters.Representation TheoryCombinatorics20C15text