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Sur la chomologie continue des representations unitaires irreductibles des groupes de lie semi-simples complexes

Part of the Lecture Notes in Mathematics book series (LNM,volume 739)

Abstract

Let G a complex connected, simply connected, semi-simple Lie group. Let , its Lie algebra, a Borel subalgebra of . To each parabolic subalgebra of , containing po, we associate a unitary irreducible representation of G, πP, which has a trivial infinitestimal character and which is unitarily induced from P. Here P denotes the parabolic subgroup of G with Lie algebra p. Moreover we have:

Here HP is the space of πP, is the number of positive roots of the pair , which do not belong to the system of roots of the pair . When the group is of rank less than 3, it is shown that every unitary irreducible representation of G with non trivial continuous cohomology is equivalent to one of the πP.

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© 1979 Springer-Verlag Berlin Heidelberg

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Delorme, P. (1979). Sur la chomologie continue des representations unitaires irreductibles des groupes de lie semi-simples complexes. In: Eymard, P., Takahashi, R., Faraut, J., Schiffmann, G. (eds) Analyse Harmonique sur les Groupes de Lie II. Lecture Notes in Mathematics, vol 739. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062492

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  • DOI: https://doi.org/10.1007/BFb0062492

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09536-1

  • Online ISBN: 978-3-540-35023-1

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