In this Note we consider examples of partially hyperbolic actions: restrictions of Weyl chamber flows on SL (n, R) / Γ (n ≥ 4). We show that generic restrictions of rank at least two are locally rigid. Our approach combines the geometry of the invariant foliations for the action and the algebraic properties of the group SL (n, R). The method is applicable to restrictions of Weyl chamber flows on other homogeneous spaces. To cite this article: D. Damjanović, A. Katok, C. R. Acad. Sci. Paris, Ser. I 344 (2007).
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