Abstract
A group G associated with the n-dimensional anisotropic harmonic oscillator is shown to be embedded in a semidirect product L of the Weyl group N and the symplectic group Sp(2n,R). A particular induced representation of the group L, when restricted to G, is proved to be unitarily equivalent to ⊕sdω,sUGv,−(sgnv)s) where dω,s is the degeneracy of the energy level Eω,s of the n-dimensional anisotropic harmonic oscillator with frequencies (ω1, ω2,...,ωn) =ω, UGv,−(sgnv)s is an irreducible representation of G, and s may be regarded as indexing all distinct energy levels of the system.
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