## Smooth representations of reductive $$p$$-adic groups: structure theory via types.(English)Zbl 0911.22014

This paper is concerned with the behavior under parabolic induction of the “type” of a connected reductive $$\ell$$-group $$G$$, and its use for classification of admissible representation [cf. I. N. Bernstein and A. V. Zelevinsky, Russ. Math. Surv. 31, 1–68 (1976); translation from Usp. Mat. Nauk 31, No. 3(189), 5–70 (1976; Zbl 0342.43017); Ann. Sci. Éc. Norm. Supér., IV. Sér. 10, 441–472 (1977; Zbl 0412.22015)] of $$G$$ (the authors refer only to unpublished notes of W. Casselman [An introduction to the theory of admissible representations of reductive $$p$$-adic groups, dated 1974], but not to the fundamental well-written publications cited above). This continues many previous papers of the authors, which are concerned mainly with $$\text{GL}(n)$$ and related groups.

### MSC:

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

### Keywords:

representations of reductive $$p$$-adic groups; types

### Citations:

Zbl 0342.43017; Zbl 0348.43007; Zbl 0412.22015
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