Essays on representations of real groups Symmetric spaces of semi-simple groups
نویسنده
چکیده
In Cartan’s original proof, the fixed point theorem was about Riemannian spaces of negative curvature, but I’ll use instead a simpler geometric notion due to [Bruhat-Tits:1972]. This allows an argument that is somewhat shorter and more direct than the standard one presented, for example, in [Helgason:1968]. The original application of the criterion of Bruhat-Tits was to buildings, as explained in [Bruhat-Tits:1972] and also the book [Brown:1989]. But Bruhat and Tits also observed that the criterion would apply to manifolds of negative curvature.
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