About: 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.

Attributes	Values
rdf:type	anatomical structure yago:WikicatLieAlgebras yago:WikicatLieGroups yago:Abstraction100002137 yago:Algebra106012726 yago:Attribute100024264 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:Group100031264 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:WikicatHomogeneousSpaces yago:Science105999797 yago:Space100028651
rdfs:label	Kostant's convexity theorem (en)
rdfs:comment	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. (en)
dcterms:subject	Lie algebras Homogeneous spaces Mathematical theorems Lie groups
Wikipage page ID	37872896 (xsd:integer)
Wikipage revision ID	955922000 (xsd:integer)
Link from a Wikipage to another Wikipage	Iwasawa decomposition Jacobi eigenvalue algorithm Lie algebras Compact Lie group Complexification Convex set Homogeneous spaces Identity component Symmetric space Calabi–Yau manifold Mathematical theorems Lie groups Golden–Thompson inequality Maximal torus Cartan subalgebra Moment map Weyl group Restricted Weyl group Coadjoint orbit
Link from a Wikipage to an external page	http://www.iumj.indiana.edu/docs/21037/21037.asp%7Cdoi=10.1512/iumj.1972.21.21037%7Cdoi-access=free https://archive.org/details/groupsgeometrica0000helg/page/473
sameAs	Kostant's convexity theorem Kostant's convexity theorem Kostant's convexity theorem Kostant's convexity theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Reflist dbt:Short_description dbt:Harvs
authorlink	Bertram Kostant (en)
first	Bertram (en)
last	Kostant (en)
year	1973 (xsd:integer)
has abstract	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. Kostant used this to generalize the Golden–Thompson inequality to all compact groups. (en)
gold:hypernym	Convex
prov:wasDerivedFrom	wikipedia-en:Kostant's_convexity_theorem?oldid=955922000&ns=0
page length (characters) of wiki page	13212 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Kostant's_convexity_theorem
is Link from a Wikipage to another Wikipage of	Bertram Kostant Schur–Horn theorem Moment map Kostant convexity theorem
is Wikipage redirect of	Kostant convexity theorem
is known for of	Bertram Kostant
is known for of	Bertram Kostant
is foaf:primaryTopic of	wikipedia-en:Kostant's_convexity_theorem

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