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On reducibility of parabolic induction. (English) Zbl 0914.22019
The subject of the paper is the investigation of reducibility of parabolically induced representations of $$\text{Sp}(2n,F)$$ and $$\text{SO}(2n+1,F)$$, where $$F$$ is a non-archimedean local field, by applying parabolic restriction to these representations. There is a variety of general results in which reducibility of induced representations is related to reducibility of representations induced from cuspidal representations. From given concrete applications I mention the determination of the composition series for representations induced from a one-dimensional representation of certain maximal parabolic subgroups. The method of this paper was used later by C. Jantzen to complete the determination of the composition series of representations induced from a one-dimensional representation of an arbitrary parabolic subgroup.

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