On Knutson's conjecture about irreducible characters of finite groups (Q1204647)

For the groups \(SL_ 2(q)\) and \(PSL_ 2(q)\) the author obtains a criterion for correctness of the Knutson conjecture [\textit{D. Knutson}, 2- rings and the representation theory of the symmetric group (Lect. Notes Math. 308) (1973; Zbl 0272.20008)]: For every character \(\chi \in \text{Irr}(G)\), a generalized character \(\lambda \in Z[\text{Irr}(G)]\) exists such that \(\chi \cdot \lambda = \rho\) (\(\rho\) is the character of the regular representation).