Abstract
Methods of computing plethysms of the fundamental unitary irreducible representations of the non-compact symplectic group Sp(2n,R) are considered. Complete results are given for the symmetrized second powers. A number of new S-function identities are reported. The stability properties of the Sp(2n,R) plethysms are noted as well as a remarkable conjugacy relation. The application of the plethysms to N-particles in an isotropic harmonic oscillator is briefly outlined.
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