## 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:

 2.2e+51 Representations of Lie and linear algebraic groups over local fields

Zbl 0412.22015
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