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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 self-adjoint 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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  • Kostant's convexity theorem
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  • 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 self-adjoint 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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  • 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 self-adjoint 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 projection to the dual of a Cartan subalgebra. Kostant used this to generalize the Golden–Thompson inequality to all compact groups.
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  • Bertram Kostant
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  • Bertram
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  • Kostant
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