R. Merris, Linearly independent permutation characters afforded by action on tensor spaces, Linear & Multilinear Algebra 6 (1978), 263-267. Math Reviews 80c:15018.

The main result of this article is that certain permutation characters of a finite group G are linearly independent. It was conjectured that these same characters span the rational valued characters of G. Fernando C. Silva [Linear & Multilinear Algebra 15 (1984), 257-263] gave necessary and sufficient conditions for the conjecture to be valid along with a counterexample to show that it does not hold in general. (The question of the existence of an irreducible counterexample does not seem to have been settled by Silva's paper.) Other work in this area appeared in