Linear preservers of Schur functions

AbstractLet Mn be the vector space of the n × n matrices over the field F. Let H be a subgroup of the symmetric group of degree n and x an F-valued character of H. If A = [aij] ϵ Mn, the Schur function of A isA is dHx(A) = ∑σϵHX(σ)Πiaiσ(i).A linear mapping T: Mn → Mn is called a Schur function preserver ifdHx(T(X)) = dHx(X)for every X in Mn.We survey some very recent results on Schur function preservers with special emphasis on the case in which H is the full symmetric group and F is the complex field. In this case a complete description of the preservers is possible