# Séparation des représentations par des surgroupes quadratiques

Abstract : 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 $G$.
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https://hal.archives-ouvertes.fr/hal-00394283
Contributor : Didier Arnal <>
Submitted on : Thursday, June 11, 2009 - 11:12:33 AM
Last modification on : Thursday, March 7, 2019 - 2:54:51 PM
Long-term archiving on : Thursday, June 10, 2010 - 10:26:44 PM

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• HAL Id : hal-00394283, version 1
• ARXIV : 0906.2057

### Citation

Didier Arnal, Mohamed Selmi, Amel Zergane. Séparation des représentations par des surgroupes quadratiques. Bulletin des Sciences Mathématiques, Elsevier, 2011, 135 (2), pp.141-165. ⟨hal-00394283⟩

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