hal-00394283, version 1
Séparation des représentations par des surgroupes quadratiques
Bulletin des Sciences Mathématiques 135, 2 (2011) 141-165
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 $G$.
- 1:
- CNRS : UMR5584 – Université de Bourgogne
- 2:
- Ecole Supérieure des Sciences et de Technologie de Hammam Sousse
- Collaboration : Accord Hubert Curien Utique 09/G 1502
- Domain : Mathematics/Representation Theory
- Keywords : Application moment – Représentations des groupes de Lie – Surgroupes quadratiques
- hal-00394283, version 1
- http://hal.archives-ouvertes.fr/hal-00394283
- oai:hal.archives-ouvertes.fr:hal-00394283
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- Submitted on: Thursday, 11 June 2009 11:12:33
- Updated on: Monday, 19 November 2012 09:37:45
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