Abstract
An exposition is given of the infinitesimal orbit theory on real affine symmetric spaces. Main references are the results by Kostant and Rallis on complex symmetric spaces and the treatment by Varadarajan of the theory of orbits under the adjoint group. Partial results are due to Oshima and Matsuki. In a final chapter we consider the problem of the existence of invariant measures on the orbits in symmetric spaces.
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