alexa REMARKS ON THE PRINCIPAL SERIES OF REPRESENTATIONS: THE CASE OF SL(2,R)
Mathematics

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): U N Bassey, O O Oyadare

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We study closely the explicit determination of the compact model of the principal series of representations of the real unimodular group which is thereafter shown to be equivalent to the induced picture Our main result shows that the compact subgroup M, encountered in the Levy-Langlands decomposition of the parabolic subgroup P, is the largest possible subgroup of that can be used in the construction of the unitary family In other words, we prove that M cannot be further enlarged in K in the methods of parabolic induction from Since minimal parabolic subgroups (which are, by definition, the K-conjugates of are the chief instruments in parabolic induction, and since a parabolic subgroup is minimal if and only if ([4, p. 536]) we see that our result is a strengthening of that of Harish-Chandra in [4]

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This article was published in JP Journal of Geometry and Topology and referenced in Journal of Generalized Lie Theory and Applications

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