Selection Rules and the Decomposition of the Kronecker Square of Irreducible Representations

Abstract

The irreducible representations occurring in the decomposition of the Kronecker squares of irreducible representations of finite and continuous groups are shown to be readily separable into symmetric and antisymmetric parts using Littlewood's method of plethysm. Particular applications of the rotation and symplectic groups, together with selection rules for isoscalar factors, are given.