JournalsprimsVol. 48, No. 4pp. 749–797

Generalized Whittaker Functions for Degenerate Principal Series of GL(4, R\mathbb R)

  • Kazuki Hiroe

    Kyoto University, Japan
Generalized Whittaker Functions for Degenerate Principal Series of GL(4, $\mathbb R$) cover
Download PDF

Abstract

For degenerate principal series representations of GL(n, R\mathbb R), we show that the spaces of corresponding class one generalized Whittaker functions are characterized by explicit systems of di erential operators. By using this characterization, we give detailed calculations on GL(4, R\mathbb R). 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, R\mathbb R). Publ. Res. Inst. Math. Sci. 48 (2012), no. 4, pp. 749–797

DOI 10.2977/PRIMS/88