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

Bushnell, Colin J.; Kutzko, Philip C.

Proc. Lond. Math. Soc., III. Ser. 77, No. 3, 582-634 (1998).

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 Sér. 10, 441–472 (1977; Zbl 0412.22015)] of \(G\) (the authors refer only to unpublished notes of W. Casselman [An introduction to the theory of admissible representations of reductive \(p\)-adic groups, dated 1974], but not to the fundamental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.

Reviewer: Yuval Z. Flicker (Columbus/Ohio)

MSC:

22E50

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