Whittaker functions for generalized principal series representations of \(\mathrm{SL}(3, \mathbb R)\) (Q1003146)

In the theory of automorphic forms, Whittaker functions (WF) are a generalization of Fourier coefficients of cuspidal modular forms. They provide important analytical tools for the study of automorphic \(L\)-functions. In the present paper WF for principal series representations of \(\text{SL}_3({\mathbb R})\) are studied. This restricted choice allows for quite explicit formulae. The latter are given for radial parts of certain WF. A set of differential equations of Lie-theoretic origin is determined, that are satisfied by WF. Formal power series solutions to these differential equations are studied. Finally, an integral representation of some WF is given.