Degenerate Representations of the Symplectic Groups II. The Noncompact Group Sp(p, q)

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Abstract
Using a method based on geometrical properties of homogeneous spaces of rank one homeomorphic to coset spaces of Lie groups, a series of degenerate unitary irreducible representations of the noncompact symplectic group Sp(p, q) is investigated. The representation spaces for a discrete series determined by two integer numbers and a continuous series determined by one real and one integer parameter are given, the corresponding basis functions being formed by the linear combinations of eigenfunctions of the Laplace‐Beltrami operator of the considered space. Explicit formulas for the action of generators of Sp(p, q) in these representations are obtained. The results provide a deeper insight into the structure of the two‐parameter ``not most degenerate'' unitary representations.

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