Harmonic analysis in one-parameter metabelian nilmanifolds.
Discrete cocompact subgroups of the five-dimensional connected and simply connected nilpotent Lie groups.
Sur les représentations mixtes des groupes de Lie résolubles exponentiels.
Let G be an exponential solvable Lie group, H and A two closed connected subgroups of G and σ a unitary and irreducible representation of H. We prove the orbital spectrum formula of the Up-Down representation ρ(G, H, A, σ) = Ind σ. When G is nilpotent, the multiplicities of such representation turns out to be uniformly infinite or finite and bounded. A necessary and sufficient condition for the finiteness of the multiplicities is given. The same results are obtained when G is exponential...
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