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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