Differential equations for principal series Whittaker functions on \(SU(2,2)\) (Q1384934)

Explicit linear partial differential equations are obtained for Whittaker functions belonging to an irreducible principal series representation of \(\text{SU}(2,2)\). The result should be compared with that of \textit{Miyazaki} and \textit{Oda} [Proc. 1993 Workshop Automorphic Forms and Related Topics, Pyungsan Inst. for Math. Sci, 59-92 (1993)] for \(\text{Sp}(2,R)\). Computer software Kan [downloadable from ftp.math.s.kobe-u.ac.jp via anonymous ftp] is used to check one has a holonomic system of PDEs of rank 8 as expected from \textit{B. Kostant} [Invent. Math. 48, 101-184 (1978; Zbl 0405.22013)].