Abstract
This paper presents representation-theoretic applications of the general theory of operator-valued Bessel functions developed in the first paper of this series. Here, the concern is with the circle of ideas relating decomposition of the Fourier transform on F k × n , F a real finite-dimensional division algebra and k ⩾ 2 n, to metaplectic representations, holomorphic discrete series, and limits of holomorphic discrete series for the group of biholomorphic automorphisms of the Siegel upper half-plane in the complexification of F n × n .
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