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Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case). (English) Zbl 0614.22005
The author classifies the irreducible unitary representations of the general linear group GL(n) over a local, non-Archimedean field. He constructs a set B so that every unitary representation is either in B or is unitarily induced from a representation in B. The representations in B are either irreducible quotients of representations induced from square integrable representations or complementary series representations. The classifications of the unitary dual is given in Langlands as well as in Zelevinski parameters.
A similar classification of the unitary dual for Archimedean fields was obtained by D. Vogan.
Reviewer: B.Speh

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