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- Hermitian_symmetric_space abstract "In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has as an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds.Every Hermitian symmetric space is a homogeneous space for its isometry group and has a unique decomposition as a product of irreducible spaces and a Euclidean space. The irreducible spaces arise in pairs as a non-compact space that, as Borel showed, can be embedded as an open subspace of its compact dual space. Harish Chandra showed that each non-compact space can be realized as a bounded symmetric domain in a complex vector space. The simplest case involves the groups SU(2), SU(1,1) and their common complexification SL(2,C). In this case the non-compact space is the unit disk, a homogeneous space for SU(1,1). It is a bounded domain in the complex plane C. The one-point compactification of C, the Riemann sphere, is the dual space, a homogeneous space for SU(2) and SL(2,C).Irreducible compact Hermitian symmetric spaces are exactly the homogeneous spaces of simple compact Lie groups by maximal closed connected subgroups which contain a maximal torus and have center isomorphic to T. There is a complete classification of irreducible spaces, with four classical series, studied by Cartan, and two exceptional cases; the classification can be deduced fromBorel–de Siebenthal theory, which classifies closed connected subgroups containing a maximal torus. Hermitian symmetric spaces appear in the theory of Jordan triple systems, several complex variables, complex geometry, automorphic forms and group representations, in particular permitting the construction of the holomorphic discrete series representations of semisimple Lie groups.".
- Hermitian_symmetric_space wikiPageExternalLink lecturenotesinma19691rice.
- Hermitian_symmetric_space wikiPageExternalLink irvine.pdf.
- Hermitian_symmetric_space wikiPageExternalLink 13028.
- Hermitian_symmetric_space wikiPageExternalLink 1968117.
- Hermitian_symmetric_space wikiPageExternalLink 2371774.
- Hermitian_symmetric_space wikiPageID "4127357".
- Hermitian_symmetric_space wikiPageRevisionID "599458941".
- Hermitian_symmetric_space hasPhotoCollection Hermitian_symmetric_space.
- Hermitian_symmetric_space subject Category:Complex_manifolds.
- Hermitian_symmetric_space subject Category:Differential_geometry.
- Hermitian_symmetric_space subject Category:Homogeneous_spaces.
- Hermitian_symmetric_space subject Category:Lie_groups.
- Hermitian_symmetric_space subject Category:Riemannian_geometry.
- Hermitian_symmetric_space type Abstraction100002137.
- Hermitian_symmetric_space type Attribute100024264.
- Hermitian_symmetric_space type Group100031264.
- Hermitian_symmetric_space type HomogeneousSpaces.
- Hermitian_symmetric_space type LieGroups.
- Hermitian_symmetric_space type Space100028651.
- Hermitian_symmetric_space comment "In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has as an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds.Every Hermitian symmetric space is a homogeneous space for its isometry group and has a unique decomposition as a product of irreducible spaces and a Euclidean space.".
- Hermitian_symmetric_space label "Hermitian symmetric space".
- Hermitian_symmetric_space sameAs m.03bxcrx.
- Hermitian_symmetric_space sameAs Q5741926.
- Hermitian_symmetric_space sameAs Q5741926.
- Hermitian_symmetric_space sameAs Hermitian_symmetric_space.
- Hermitian_symmetric_space wasDerivedFrom Hermitian_symmetric_space?oldid=599458941.
- Hermitian_symmetric_space isPrimaryTopicOf Hermitian_symmetric_space.