Shift operators and factorial symmetric functions

A new class of symmetric functions called factorial Schur symmetric functions has recently been discovered in connection with a branch of mathematical physics. We align this theory more closely with the standard symmetric function theory, giving the factorial Schur function a tableau definition, introducing a shift operator and a new generating function with which we extend to factorial symmetric functions proofs of various determinantal identities for classical symmetric functions, and defining a new factorial symmetric function—the factorial elementary symmetric function.