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The diagonal distribution for the invariant measure of a unitary type symmetric space

Doug Pickrell
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Abstract

Let U denote a simply connected compact Lie group, let K denote the fixed point set for an involutive automorphism of U, and let m denote the U-invariant probability measure on the symmetric space U/K. Consider the geodesic embedding U/K into U of Cartan. In this paper we compute the diagonal distribution for m, relative to a compatible triangular decomposition of G, the complexification of U. This boils down to a Duistermaat-Heckman exact stationary phase calculation, involving a Poisson structure on the dual symmetric space G_0/K discovered by Evens and Lu.

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Doug Pickrell. 2005-06-14. The diagonal distribution for the invariant measure of a unitary type symmetric space. https://arxiv.org/abs/math/0506283

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