A method for obtaining symmetrized representations of SU(2)×SU(2) and the rotation group SO(4)

Abstract

A formula is obtained by which any symmetrized power of (j1,j2) may be expressed in terms of symmetrized powers of representations belonging to lower j values. In particular formulae are obtained for (1/2,J)(X)(2) and (1,J)(X)(2). The method is generalized to cover groups of the form SU(2)*SU(2)*...(r times). This problem has application to the L-S coupling shell model of nuclear physics.