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Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whosenilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We studythe degenerate principal series representations of $G$ on $C^\infty(X)$ in thecase where $P$ is not conjugate to its opposite parabolic. We find the pointsof reducibility, the composition series and all unitarizable constituents.Among the unitarizable constituents we identify some small representationshaving as associated variety the minimal nilpotent $K_{\mathbb{C}}$-orbit in$\mathfrak{p}_{\mathbb{C}}^*$, where $K_{\mathbb{C}}$ is the complexificationof a maximal compact subgroup $K\subseteq G$ and$\mathfrak{g}=\mathfrak{k}+\mathfrak{p}$ the corresponding Cartandecomposition.

Structure of the degenerate principal series on symmetric R-spaces and small representations