AbstractsPhysics

We find the generating function for group tensors contained in the enveloping algebra of each simple compact group of rank three or less. The generating function depends on dummy variables which carry, as exponents, the degrees and representation labels of the tensors; it suggests an integrity basis, a finite number of elementary tensors, in terms of which all can be expressed as stretched tensor products. We show how the generating functions for tensors in the enveloping algebra of SO(5) and SU(3) reduce when the tensors are acting on the basis of representations for which one of the Cartan labels vanish. The missing label problem in the reduction SO(5) (R-HOOK) SO(3) restricted to SO(5) representations of the type (0,(nu)) is considered; the eigenvalues and eigenvectors of a missing label operator are found up to (including) representation (0,12).