Kostant's convexity theorem, introduced by Bertram Kostant in 1973, states that the projection of any coadjoint orbit of a connected compact Lie group onto the dual of a Cartan subalgebra forms a convex set, a special case of a more general convexity result for symmetric spaces. It generalizes an earlier result of Schur, Horn, and Thompson for Hermitian matrices, which showed that projecting the set of self-adjoint matrices with fixed eigenvalues onto their diagonal entries produces the convex polytope whose vertices are all permutations of those eigenvalues, and it can be used to derive Lie-theoretic extensions of the Golden-Thompson inequality and the Schur-Horn theorem.
Facts
StatementThe projection of every coadjoint orbit of a connected compact Lie group into the dual of a Cartan subalgebra is a convex set. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Kostant's convexity theorem - Wikipedia
Introduction, paragraph 2, sentence 1
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.
Lead paragraph
introduced by Bertram Kostant (1973)
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