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Let $\pi$ be an unitary irreducible representation of a Lie group $G$. $\pi$defines a moment set $I_\pi$, subset of the dual $\mathfrak g^*$ of the Liealgebra of $G$. Unfortunately, $I_\pi$ does not characterize $\pi$. However, wesometimes can find an overgroup $G^+$ for $G$, and associate, to $\pi$, arepresentation $\pi^+$ of $G^+$ in such a manner that $I_{\pi^+}$ characterizes$\pi$, at least for generic representations $\pi$. If this construction isbased on polynomial functions with degree at most 2, we say that $G^+$ is aquadratic overgroup for $G$. In this paper, we prove the existence of such aquadratic overgroup for many different classes of $G$.

S\'eparation des repr\'esentations par des surgroupes quadratiques