Realisation of Lie algebras and of representations of Lie groups in terms of harmonic oscillators

The algebras and irreducible representations (irreps) of compact Lie groups, including the exceptional groups, are realised in terms of sets of Bose oscillator (SHO) creation and annihilation operators. In particular, not only the tensor irreps, but also the spinor irreps of orthogonal groups of all ranks can be constructed using Bose (rather than the more customary Fermi) oscillators. (author)