\(L^ 2\)-versions of the Howe correspondence. II
[Part I of this paper will appear in Math. Scand.] We present the explicit decomposition of the space of \(L^2\)-sections of vector bundles over the projective complex and quaternion hyperboloids. Using this we further calculate the \(L^2\) decompositions of the metaplectic representations for the dual pairs \(SL (2, \mathbb{R}) \times O(p,q)\), \(U(1,1) \times U (p,q)\) and \(O^* (4) \times Sp (p,q)\) by extending the idea of pluriharmonic functions due to M. Kashiwara and M. Vergne.
scientific article; zbMATH DE number 891038