Symmetrized Kronecker Products of Group Representations

Abstract

Certain phases are associated with the Kronecker squares and cubes of representations of the finite and of the compact semi-simple groups. These phases are important in giving the symmetry properties of the 1 — jm and 3 — jm symbols of the groups [4; 9]. It is our primary purpose to evaluate these phases. The Frobenius-Schur invariant [12, p. 142] for an irreducible representation of group G (1.1)