Journal of Lie Theory
Vol. 8, No. 2, pp. 311-324 (1998)

Restrictions a un sous-espace de Cartan des fonctions ${\cal C}^\infty$ invariantes sur l'espace tangent d' un espace symetrique

N. Kamoun

Departement de Mathematiques,
Faculte des Sciences,
5019 Monastir,

Abstract: Let $G$ be a real connected reductive Lie group, $\sigma$ an involution of $G$, and $H$ the identity component of the group of its fixed points. Let $\scriptstyle{\g g}$ denote the Lie algebra of $G$, $\scriptstyle{\g g}={\g h}\oplus {\g q}$ its decomposition into $\pm 1$-eigenspaces for $\sigma$, and $\scriptstyle{\g a}$ a Cartan subspace of $\scriptstyle{\g q}$. We study the restriction to $\scriptstyle{\g a}$ of $H$-invariant differentiable functions on $\scriptstyle{\g q}$, and we give a description of the image of this map.

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