Bessel Functions on Quaternionic Siegel Domains

This paper applies the theory of operator-valued Bessel functions on Schrödinger-Fock spaces and Siegel domains of type II developed in (H. Ding, J. Funct. Anal.106 (1992), 189-225) to harmonic analysis on quaternionic Hermitian symmetric spaces and the representation theory of the groups O*(2m) for m odd. Using the reduced Bessel function Kπ we study the harmonic representation and holomorphic discrete series for these groups.