Abstract
Let G be a simple real Lie group with maximal parabolic subgroup P whose nilradical is abelian. Then X=G/P is called a symmetric R-space. We study the degenerate principal series representations of G on C∞(X) in the case where P is not conjugate to its opposite parabolic. We find the points of reducibility, the composition series and all unitarizable constituents. Among the unitarizable constituents we identify some small representations having as associated variety the minimal nilpotent KC-orbit in pC⁎, where KC is the complexification of a maximal compact subgroup K⊆G and g=k+p the corresponding Cartan decomposition.
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