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We show that the elementary modes of the planar harmonic oscillator can bequantised in the framework of quantum mechanics based on pseudo-hermitianhamiltonians. These quantised modes are demonstrated to act as dynamicalstructures behind a new Jordan - Schwinger realization of the SU(1,1) algebra.This analysis complements the conventional Jordan - Schwinger construction ofthe SU(2) algebra based on hermitian hamiltonians of a doublet of oscillators.

$PT$ symmetry and a dynamical realization of the SU(1,1) algebra