Linear preservers of Schur functions Original Research Article

Let Mn be the vector space of the n × n matrices over the field image. Let H be a subgroup of the symmetric group of degree n and x an image-valued character of H. If A = [aij] ε Mn, the Schur function of A is A is image. A linear mapping T: Mn → Mn is called a Schur function preserver if imagedHx(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 image is the complex field. In this case a complete description of the preservers is possible.