SHIFT-OPERATORS AND FACTORIAL SYMMETRICAL FUNCTIONS

A new class of symmetric functions called factorial Schur symmetric fu nctions has recently been discovered in connection with a branch of ma thematical physics. We align this theory more closely with the standar d symmetric function theory, giving the factorial Schur function a tab leau definition, introducing a shift operator and a new generating fun ction with which we extend to factorial symmetric functions proofs of various determinantal identities for classical symmetric functions, an d defining a new factorial symmetric function-the factorial elementary symmetric function. (c) 1995 Academic Press, Inc.