Discrete series characters for \(\text{GL}(n,q)\) (Q1294012)

The `discrete series' characters of the finite general linear group \(\text{GL}(n,q)\) are those ordinary, irreducible characters which are not constituents of the permutation character induced from the radical of any proper parabolic subgroup of \(\text{GL}(n,q)\). They cannot be obtained by `Harish-Chandra induction' from characters of \(\text{GL}(n',q)\) for \(n'<n\), nor expressed as linear combinations of characters induced from proper parabolic subgroups of \(\text{GL}(n,q)\). Various methods are known for calculating these discrete series characters but the paper under review presents them in a particularly simple fashion, as \(\mathbb{Z}\)-linear combinations of characters induced from linear characters on certain subgroups of \(\text{GL}(n,q)\).