Bessel functions and representation theory, II holomorphic discrete series and metaplectic representations

AbstractThis 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 Fk × n, F a real finite-dimensional division algebra and k ⩾ 2n, 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 Fn × n