For degenerate principal series representations of GL(n, ), we show that the spaces of corresponding class one generalized Whittaker functions are characterized by explicit systems of dierential operators. By using this characterization, we give detailed calculations on GL(4, ). We examine the dimensions of the spaces of generalized Whittaker functions and give their generators in terms of hypergeometric functions of one and two variables. We show that generalized Whittaker functions have multiplicity one by using the theory of hypergeometric functions.
Cite this article
Kazuki Hiroe, Generalized Whittaker Functions for Degenerate Principal Series of GL(4, ). Publ. Res. Inst. Math. Sci. 48 (2012), no. 4, pp. 749–797DOI 10.2977/PRIMS/88