The matrix representations of g2. II. Representations in an su(3) basis

Abstract

Irreducible representations of the real compact Lie algebra g2 are given in g2⊇ su(3) bases. A missing label is accounted for by the explicit construction of a g2⊇ su(3) basis of vector holomorphic functions. Analytical results are given for two multiplicity-free classes of irreps. It is also shown how vector coherent state (VCS) theory accommodates the decomposition of the nilpotent raising operator subalgebra of an arbitrary Lie algebra into a finite but arbitrary number of irreducible tensorial sets under transformations generated by a stability algebra.