Abstract
It is shown that O(p,q) and Sp(2,R) are complementary groups in the space of pseudo-oscillator Hpq eigenfunctions. The structure and irreducible representation of both invariancy algebra and generating-spectrum algebra are discussed in detail. It is proved that the transformation brackets between the basis diagonalising the compact generator and the basis diagonalising the non-compact generator in the case of discrete series of irreducible representations of the SU(1,1) group coincide with the Clebsch-Gordan coefficients for the Kronecker product D14+/(X)D14-/ of two irreducible representations of the SU(1,1) group belonging to positive and negative discrete series respectively.
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