We introduce a basis of the symmetric functions that evaluates to (irreducible) characters group, just as Schur evaluate irreducible G L n modules. Our main result gives three different characterizations for this basis. One shows structure coefficients (outer) product these are stable Kronecker coefficients. The results in paper focus on developing fundamental properties

Under reasonable assumptions, a group action on module extends to the minimal free resolutions of module. Explicit descriptions these actions can lead better understanding by providing, for example, convenient expressions their differentials or alternative characterizations Betti numbers. This article introduces an algorithm computing characters finite groups acting finitely generated graded mo...