In mathematics, Kostant's convexity theorem, introduced by Bertram Kostant (), states that the projection of every coadjoint orbit of a connected compact Lie group into the dual of a Cartan subalgebra is a convex set. It is a special case of a more general result for symmetric spaces. Kostant's theorem is a generalization of a result of , and for hermitian matrices. They proved that the projection onto the diagonal matrices of the space of all n by n complex selfadjoint matrices with given eigenvalues Λ = (λ1, ..., λn) is the convex polytope with vertices all permutations of the coordinates of Λ. In fact this result is 'Kostant's linear convexity theorem'; the main focus of Kostant () is Kostant's nonlinear convexity theorem which involves the Iwasawa projection rather than the linear p
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