Jacquet functors and unrefined minimal \(K\)-types. (English) Zbl 0860.22006

Moy, Allen; Prasad, Gopal

Comment. Math. Helv. 71, No. 1, 98-121 (1996).

The authors define the notion of unrefined minimal \(K\)-type for a reductive group defined over a non-archimedean local field. They further define the depth of a representation. The authors determine the relationship between unrefined minimal \(K\)-types and the Jacquet functors. Analogues of fundamental results of Borel are proved for representations of depth zero.

Reviewer: V.Lakshmibai (Boston)

MSC:

22E35	Analysis on \(p\)-adic Lie groups
20G25	Linear algebraic groups over local fields and their integers

Keywords:

minimal \(K\)-type; reductive group; non-archimedean local field; representation; Jacquet functors