On the degenerate principal series of complex symplectic groups

We apply techniques introduced by Clerc, Kobayashi, Ørsted and Pevzner to study the degenerate principal series of Sp(n,C). An explicit description of the K-types is provided and Knapp–Stein normalised operators are realised as symplectic Fourier transforms, and their K-spectrum explicitly computed. Reducibility phenomena are analysed in terms of K-types and eigenvalues of intertwining operators. We also construct a new model for these representations, in which Knapp–Stein intertwiners take an algebraic form.