Bessel Functions on Quaternionic Siegel Domains

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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 *(2 m) for m odd. Using the reduced Bessel function K π we study the harmonic representation and holomorphic discrete series for these groups.