The Whittaker models of induced representations. (English) Zbl 0535.22017

Jacquet, Hervé; Shalika, Joseph

Pac. J. Math. 109, 107-120 (1983).

In the paper the authors receive the following main general results. Every irreducible admissible representation \(\pi\) of the group GL(n,F) is a quotient of a representation \(\xi\) induced by a tempered one. Here F is a local non-Archimedean field, \(n\geq 2\), \(n\in {\mathbb{Z}}\). In addition the authors show that \(\xi\) has a Whittaker model, even though it may fail to be irreducible. Earlier similar results were well known only in the special case \(n=2\). On this subject see also the paper of I. N. Bernstein and A. V. Zelevinsky [Ann. Sci. Ex. Norm. Supér., IV. Sér. 10, 441-472 (1977; Zbl 0412.22015)].

Reviewer: A.Venkov

MSC:

22E50

Representations of Lie and linear algebraic groups over local fields

Keywords:

induced representations; tempered representations; Whittaker model; admissible representation