The contraction of S^2p-1 to H^p-1

A contraction of the sphere S^{2p 1}, considered as the homogeneous space U(p)/U(p - 1), to the Heisenherg group H^p-1 is defined. The infinite dimensional irreducible unitary representations of Heisenberg group H^p-1 are then shown to be the limits of the irreducible representations of U(p) which are class-1 with respect to U(p - 1). Our results generalise the earlier results of Fulvio Ricci.