%0 Journal Article
%T S¨¦paration des repr¨¦sentations par des surgroupes quadratiques
%A Didier Arnal
%A Mohamed Selmi
%A Amel Zergane
%J Mathematics
%D 2009
%I arXiv
%X 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 Lie algebra of $G$. Unfortunately, $I_\pi$ does not characterize $\pi$. However, we sometimes can find an overgroup $G^+$ for $G$, and associate, to $\pi$, a representation $\pi^+$ of $G^+$ in such a manner that $I_{\pi^+}$ characterizes $\pi$, at least for generic representations $\pi$. If this construction is based on polynomial functions with degree at most 2, we say that $G^+$ is a quadratic overgroup for $G$. In this paper, we prove the existence of such a quadratic overgroup for many different classes of $G$.
%U http://arxiv.org/abs/0906.2057v1