Singular unitary highest weight representations via geometric quantization

We report on a joint work with K.-H. Neeb and B. Ørsted (cf. [5–8]) on a geometric construction of singular unitary highest weight representations based on Kirillovʹs orbit method. In the case of scalar lowest K-type we obtain all unitary highest weight representations. In the vector case we have some preliminary results extending work of J. L. Clerc (cf. [1]) on operator valued Laplace transforms.