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

MSC:
22E35 Analysis on \(p\)-adic Lie groups
20G25 Linear algebraic groups over local fields and their integers
MathOverflow Questions:
Iwahori decomposition of general groups
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