Principal series Whittaker functions on \(\operatorname {Sp}(2;\mathbb{R})\). II (Q1273499)

The authors obtain explicit formulae for the radial part of the Whittaker functions on \(G= \text{Sp} (2,\mathbb{R})\) belonging to principal series representations induced from the maximal parabolic of \(G\) associated to the long simple root. The characterization of the radial part of these functions follows from a detailed study of the action of Schmid's differential operators on spaces of Whittaker functions of a given \(K\)-type. The authors have previous results of this nature for Whittaker functions attached to various admissible representations of the real symplectic group of rank 2 [see Automorphic forms and related topics, Seoul 1993, 59-92 (1994; Zbl 0958.11037)].