Overalgebras and separation of generic coadjoint orbits of $SL(n, \R)$

Abstract : For the semi simple and deployed Lie algebra $\mathfrak g=\mathfrak{sl}(n, \R)$, we give an explicit construction of an overalgebra $\mathfrak g^+=\mathfrak g\rtimes V$ of $\mathfrak g$, where $V$ is a finite dimensional vector space. In such a setup, we prove the existence of a map $\Phi$ from the dual $\mathfrak g^\star$ of $\mathfrak g$ into the dual $(\mathfrak g^+)^\star$ of $\mathfrak g^+$ such that the coadjoint orbits of $\Phi(\xi)$, for generic $\xi$ in $\mathfrak g^\star$, have a distinct closed convex hulls. Therefore, these closed convex hulls separate 'almost' the generic coadjoint orbits of $G$.
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Submitted on : Thursday, June 21, 2012 - 10:13:02 AM
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  • HAL Id : hal-00710555, version 1
  • ARXIV : 1206.4982

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Amel Zergane. Overalgebras and separation of generic coadjoint orbits of $SL(n, \R)$. 2012. ⟨hal-00710555⟩

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