Generating functions for SU(2) plethysms with fixed exchange symmetry

Abstract

A number of fixed-plethysm generating are given for SU(2); a fixed -plethysm generating function gives the content of the component with definite exchange symmetry of the direct product of a given number of copies of an irreducible representation Rl, with l running through all values. New symmetries are found relating antisymmetric to symmetric products, and relating plethysms in which the number of factors is interchanged with the factor representation label l. Expressions for two-box plethysm generating function for SU(3) and for fixed-plethysm generating functions for SU(2) based on reducible representations are also given.