×

zbMATH — the first resource for mathematics

The Whittaker models of induced representations. (English) Zbl 0535.22017
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
PDF BibTeX XML Cite
Full Text: DOI