Harmonic Analysis on the Quotient Spaces of Heisenberg Groups, II Original Research Article

This article is a continuation of a previous article by the author [Harmonic analysis on the quotient spaces of Heisenberg groups, Nagoya Math. J.123 (1991), 103-117]. In this article, we construct an orthonormal basis of the irreducible invariant component H(image)Ω [A0] of the Hilbert space L2(H(g, h)R\H(g, h)R) in the previous article and also construct a nonholomorphic modular form of half integral weight using the Hermite functions.