An integral transform and ladder representations of U(p,q)

John D. Lorch

Vol. 186 (1998), No. 1, 89–109

DOI: 10.2140/pjm.1998.186.89

Abstract

The positive spin ladder representations of G = U(p,q), which occur naturally on a Fock space ℱ^p,q, can each be realized within a space of polynomial-valued functions on the bounded realization D_p,q of G∕K. This is achieved via an integral transform constructed by Mantini, 1985. An inversion formula is given for Mantini’s transform. Then, natural unitary structures are obtained for the geometric realizations of the positive spin ladder representations over G∕K by using the inversion formula to pull the representations back to the Fock space setting, where the unitary structures are well-known.

Milestones

Received: 2 April 1997

Published: 1 November 1998