Principal series and generalized principal series Whittaker functions with peripheral K-types on the real symplectic group of rank 2

摘要

First, we give some explicit formulas of principal series Whittaker functions on the real symplectic group of rank 2 with arbitrary one-dimensional K-types. These formulas are extension of Ishii's formulas for Whittaker functions with minimal K-types. Secondly, we compute explicit formulas of the holonomic system for the radial part of Whittaker functions with peripheral K-types belonging to the generalized principal series representations induced from the Siegel maximal parabolic subgroup (i. e., P_S-series). Thirdly, we derive eight power series solutions for our holonomic system utilizing the embedding of the PS-series into various principal series, from the power series Whittaker functions belonging to the principal series.