Inversion of an integral transform and ladder representations of U(1,q)

Abstract

An integral transform for G=U(1,q) is studied. The transform maps the positive spin ladder representations of G on a Bargmann-Segal-Fock space F_n^1,q into a space of polynomial-valued functions on the bounded realization B^q of G/K. An inversion is given for the transform and unitary structures are given for the geometric realization of the positive spin ladder representations over G/K.