Annales de l'Institut Fourier, ISSN 0373-0956, 2016, Volume 66, Issue 1, pp. 143 - 174

In this paper we investigate invariant domains in Xi(+), a distinguished G-invariant, Stein domain in the complexification of an irreducible Hermitian...

Lie group complexification | Hermitian symmetric space | Envelope of holomorphy | Invariant Stein domain | invariant Stein domain | MATHEMATICS | envelope of holomorphy | REPRESENTATIONS | EXTENSIONS | DOMAINS | GEOMETRY

Lie group complexification | Hermitian symmetric space | Envelope of holomorphy | Invariant Stein domain | invariant Stein domain | MATHEMATICS | envelope of holomorphy | REPRESENTATIONS | EXTENSIONS | DOMAINS | GEOMETRY

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2014, Volume 278, Issue 3, pp. 769 - 793

We carry out a detailed study of $$\Xi ^+$$ Ξ + , a distinguished $$G$$ G -invariant Stein domain in the complexification of an irreducible Hermitian symmetric...

Lie group complexification | Hermitian symmetric space | 32M05 | Mathematics, general | Mathematics | 32Q28 | Invariant Stein domain | MATHEMATICS | GEOMETRY

Lie group complexification | Hermitian symmetric space | 32M05 | Mathematics, general | Mathematics | 32Q28 | Invariant Stein domain | MATHEMATICS | GEOMETRY

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 06/2014, Volume 266, Issue 11, pp. 6599 - 6618

In this paper an extended Corach–Porta–Recht decomposition theorem for Finsler symmetric spaces of semi-negative curvature in the context of reductive...

Complexification | Reductive structure | Flag manifold | Operator decomposition | Stiefel manifold | Corach–Porta–Recht decomposition | Coadjoint orbit | Banach–Lie group | Finsler structure | Homogeneous space | Corach-Porta-Recht decomposition | Banach-Lie group | THEOREM | MATHEMATICS | CURVATURE | MANIFOLDS

Complexification | Reductive structure | Flag manifold | Operator decomposition | Stiefel manifold | Corach–Porta–Recht decomposition | Coadjoint orbit | Banach–Lie group | Finsler structure | Homogeneous space | Corach-Porta-Recht decomposition | Banach-Lie group | THEOREM | MATHEMATICS | CURVATURE | MANIFOLDS

Journal Article

Pramana - Journal of Physics, ISSN 0304-4289, 10/2009, Volume 73, Issue 4, pp. 627 - 637

A new kind of PT and non-PT-symmetric complex potentials are constructed from a group theoretical viewpoint of the sl(2, C) potential algebras. The real...

Lie algebra, PT symmetry | Regular eigenfunctions | Non-Hermitian Hamiltonians | Real eigenvalues | EIGENVALUES | REAL SPECTRUM | PHYSICS, MULTIDISCIPLINARY | ALGEBRA | real eigenvalues | SYMMETRIC QUANTUM-MECHANICS | Lie algebra | PT symmetry | regular eigenfunctions | PSEUDO-HERMITICITY

Lie algebra, PT symmetry | Regular eigenfunctions | Non-Hermitian Hamiltonians | Real eigenvalues | EIGENVALUES | REAL SPECTRUM | PHYSICS, MULTIDISCIPLINARY | ALGEBRA | real eigenvalues | SYMMETRIC QUANTUM-MECHANICS | Lie algebra | PT symmetry | regular eigenfunctions | PSEUDO-HERMITICITY

Journal Article

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Full Text
A remark on the orbit structure of the complexification of a semisimple symmetric space

Differential Geometry and its Applications, ISSN 0926-2245, 04/2012, Volume 30, Issue 2, pp. 195 - 205

We consider the action of a real semisimple Lie group G on the complexification GC/HC of a semisimple symmetric space G/H and we present a refinement of...

Complexification | Slice representation | Orbit structure | Semisimple symmetric space | MATHEMATICS | INVOLUTIONS | MATHEMATICS, APPLIED | LIE-GROUPS | EXTENSIONS | DOMAINS | Isotropy | Equivalence | Mathematical analysis | Differential geometry | Roots | Lie groups | Orbits | Representations

Complexification | Slice representation | Orbit structure | Semisimple symmetric space | MATHEMATICS | INVOLUTIONS | MATHEMATICS, APPLIED | LIE-GROUPS | EXTENSIONS | DOMAINS | Isotropy | Equivalence | Mathematical analysis | Differential geometry | Roots | Lie groups | Orbits | Representations

Journal Article

Journal of Generalized Lie Theory and Applications, ISSN 1736-4337, 2016, Volume s2

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 12/2008, Volume 238, Issue 2, pp. 275 - 330

Let G/K be a noncompact, rank-one, Riemannian symmetric space, and let G(C) be the universal complexification of G. We prove that a holomorphically separable,...

Riemann domain | Symmetric space | Semisimple Lie group | MATHEMATICS | LIE-GROUPS | semisimple Lie group | ENVELOPES | HOLOMORPHIC EXTENSIONS | symmetric space | INVARIANT DOMAINS | STEIN-SPACES | GEOMETRY

Riemann domain | Symmetric space | Semisimple Lie group | MATHEMATICS | LIE-GROUPS | semisimple Lie group | ENVELOPES | HOLOMORPHIC EXTENSIONS | symmetric space | INVARIANT DOMAINS | STEIN-SPACES | GEOMETRY

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 11/2003, Volume 355, Issue 11, pp. 4581 - 4594

Let M=G/K be a homogeneous Riemannian manifold with \dim_{\mathbb{C}} G^{\mathbb{C}} = \dim_{\mathbb{R}} G, where G^{\mathbb{C}} denotes the universal...

Mathematical domains | Tangents | Riemann manifold | Algebra | Lie groups | Coordinate systems | Power series | Level curves | Symmetry | Homogeneous Riemannian spaces | Stein manifold | Adapted complex structure | MATHEMATICS | homogeneous Riemannian spaces | EXTENSIONS | SPACES | GRAUERT TUBES | COMPLEX STRUCTURES | adapted complex structure | MONGE-AMPERE EQUATION

Mathematical domains | Tangents | Riemann manifold | Algebra | Lie groups | Coordinate systems | Power series | Level curves | Symmetry | Homogeneous Riemannian spaces | Stein manifold | Adapted complex structure | MATHEMATICS | homogeneous Riemannian spaces | EXTENSIONS | SPACES | GRAUERT TUBES | COMPLEX STRUCTURES | adapted complex structure | MONGE-AMPERE EQUATION

Journal Article

Journal of Algebra, ISSN 0021-8693, 05/2002, Volume 251, Issue 2, pp. 619 - 685

Let G/K be a noncompact Riemannian symmetric space and let GC/KC be its complexification. Then G acts on GC/KC by left translations. We study the invariant...

symmetric space | homogeneous CR-structure | semisimple Lie group | Semisimple lie group | Symmetric space | Homogeneous CR-structure | MATHEMATICS | GRAUERT TUBES | ORBITS | MANIFOLDS | COMPLEX STRUCTURES | MONGE-AMPERE EQUATION

symmetric space | homogeneous CR-structure | semisimple Lie group | Semisimple lie group | Symmetric space | Homogeneous CR-structure | MATHEMATICS | GRAUERT TUBES | ORBITS | MANIFOLDS | COMPLEX STRUCTURES | MONGE-AMPERE EQUATION

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 10/2004, Volume 15, Issue 8, pp. 735 - 747

Let G=(ℝ,+) act by biholomorphisms on a Stein manifold X which admits the Bergman metric. We show that X can be regarded as a G-invariant domain in a...

Stein manifolds | Lie group actions | Bergman metric | Complexifications | MATHEMATICS | complexifications

Stein manifolds | Lie group actions | Bergman metric | Complexifications | MATHEMATICS | complexifications

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2013, Volume 2013, Issue 16, pp. 3678 - 3721

We construct a model for the string group as an infinite-dimensional Lie group. In a second step, we extend this model by a contractible Lie group to a Lie...

DIMENSIONAL LIE-GROUPS | MATHEMATICS | PRINCIPAL BUNDLES | UNIVERSAL COMPLEXIFICATIONS | STACKS | 2-GROUPS | L-INFINITY-ALGEBRAS | NON-ABELIAN EXTENSIONS

DIMENSIONAL LIE-GROUPS | MATHEMATICS | PRINCIPAL BUNDLES | UNIVERSAL COMPLEXIFICATIONS | STACKS | 2-GROUPS | L-INFINITY-ALGEBRAS | NON-ABELIAN EXTENSIONS

Journal Article

Transformation Groups, ISSN 1083-4362, 6/2012, Volume 17, Issue 2, pp. 499 - 512

Given a holomorphic line bundle over the complex affine quadric Q 2, we investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant...

Topological Groups, Lie Groups | Mathematics | Algebra | MATHEMATICS | Holomorphic line bundle | COMPLEXIFICATION | SPACES | Kobayashi hyperbolicity | Stein manifold | Questions and answers | Mathematics - Complex Variables

Topological Groups, Lie Groups | Mathematics | Algebra | MATHEMATICS | Holomorphic line bundle | COMPLEXIFICATION | SPACES | Kobayashi hyperbolicity | Stein manifold | Questions and answers | Mathematics - Complex Variables

Journal Article

Compositio Mathematica, ISSN 0010-437X, 11/2005, Volume 141, Issue 6, pp. 1551 - 1577

We show that every countable direct system of finite-dimensional real or complex Lie groups has a direct limit in the category of Lie groups modelled on...

Regular lie group | Direct limit | Convenient differential calculus | Infinite-dimensional lie group | Integration of lie algebras | Inductive limit | Enlargeability | Extension of charts | Homogeneous space | Universal complexification | Locally finite lie algebra | INDUCTIVE LIMITS | TOPOLOGIES | FIELDS | UNIVERSAL COMPLEXIFICATIONS | infinite-dimensional Lie group | locally finite Lie algebra | convenient differential calculus | direct limit | MATHEMATICS | integration of Lie algebras | regular Lie group | enlargeability | principal bundle | universal complexification | MANIFOLDS | inductive limit | homogeneous space | extension of charts

Regular lie group | Direct limit | Convenient differential calculus | Infinite-dimensional lie group | Integration of lie algebras | Inductive limit | Enlargeability | Extension of charts | Homogeneous space | Universal complexification | Locally finite lie algebra | INDUCTIVE LIMITS | TOPOLOGIES | FIELDS | UNIVERSAL COMPLEXIFICATIONS | infinite-dimensional Lie group | locally finite Lie algebra | convenient differential calculus | direct limit | MATHEMATICS | integration of Lie algebras | regular Lie group | enlargeability | principal bundle | universal complexification | MANIFOLDS | inductive limit | homogeneous space | extension of charts

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2001, Volume 353, Issue 6, pp. 2531 - 2556

Generalizing Hermitian and pseudo-Hermitian spaces, we define {\em twisted complex symmetric spaces}, and we show that they correspond to an algebraic object...

Morphisms | Homomorphisms | Tensors | Algebra | Logical proofs | Functors | Curvature | Automorphisms | Symmetry | Complexification | Symmetric space | Jordan and lie triple system | MATHEMATICS | symmetric space | Jordan and Lie triple system | complexification

Morphisms | Homomorphisms | Tensors | Algebra | Logical proofs | Functors | Curvature | Automorphisms | Symmetry | Complexification | Symmetric space | Jordan and lie triple system | MATHEMATICS | symmetric space | Jordan and Lie triple system | complexification

Journal Article

Mathematische Annalen, ISSN 0025-5831, 6/2011, Volume 350, Issue 2, pp. 455 - 474

In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact,...

32Q15 | 53D50 | 81S10 | Mathematics, general | Mathematics | 53D25 | 32D15 | MATHEMATICS | COMPLEXIFICATIONS | GEOMETRIC-QUANTIZATION | GRAUERT TUBES | COHERENT-STATE TRANSFORM | COMPACT LIE-GROUPS | TANGENT BUNDLE | GAUGE FIELD-THEORY | SEGAL-BARGMANN TRANSFORM | MONGE-AMPERE EQUATION | RIEMANNIAN-MANIFOLDS

32Q15 | 53D50 | 81S10 | Mathematics, general | Mathematics | 53D25 | 32D15 | MATHEMATICS | COMPLEXIFICATIONS | GEOMETRIC-QUANTIZATION | GRAUERT TUBES | COHERENT-STATE TRANSFORM | COMPACT LIE-GROUPS | TANGENT BUNDLE | GAUGE FIELD-THEORY | SEGAL-BARGMANN TRANSFORM | MONGE-AMPERE EQUATION | RIEMANNIAN-MANIFOLDS

Journal Article

Iraqi Journal of Science, ISSN 0067-2904, 05/2019, Volume 60, Issue 4, pp. 856 - 858

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2008, Volume 255, Issue 10, pp. 2888 - 2932

Representations of Banach–Lie groups are realized on Hilbert spaces formed by sections of holomorphic homogeneous vector bundles. These sections are obtained...

[formula omitted]-algebra | Conditional expectation | Reproducing kernel | Similarity orbit | Amenable Banach algebra | Homogeneous vector bundle | Stinespring dilation | Geometric analysis | Representation | Banach–Lie group | Banach-Lie group | algebra | SPACES | THEOREM | CSTAR-ALGEBRAS | SIMILARITY PROBLEM | CURVATURE INVARIANT | MATHEMATICS | COMPLEXIFICATIONS | STAR-ALGEBRAS | MANIFOLDS | INDEX | COMPLEX STRUCTURES | C-algebra

[formula omitted]-algebra | Conditional expectation | Reproducing kernel | Similarity orbit | Amenable Banach algebra | Homogeneous vector bundle | Stinespring dilation | Geometric analysis | Representation | Banach–Lie group | Banach-Lie group | algebra | SPACES | THEOREM | CSTAR-ALGEBRAS | SIMILARITY PROBLEM | CURVATURE INVARIANT | MATHEMATICS | COMPLEXIFICATIONS | STAR-ALGEBRAS | MANIFOLDS | INDEX | COMPLEX STRUCTURES | C-algebra

Journal Article

岐阜大学教育学部研究報告. 自然科学, ISSN 0533-9529, 03/2004, Volume 28, pp. 79 - 88

Journal Article

manuscripta mathematica, ISSN 0025-2611, 05/2006, Volume 120, Issue 1, pp. 1 - 25

Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G/H) contains a maximal G-invariant neighbourhood Ω of the zero section where...

Geometry | Topological Groups, Lie Groups | Mathematics, general | Algebraic Geometry | Calculus of Variations and Optimal Control | Mathematics | Number Theory | Optimization | MATHEMATICS | COMPLEXIFICATIONS | REPRESENTATIONS | HOLOMORPHIC EXTENSIONS | GRAUERT TUBES | INVARIANT DOMAINS | STEIN EXTENSIONS | GEOMETRY

Geometry | Topological Groups, Lie Groups | Mathematics, general | Algebraic Geometry | Calculus of Variations and Optimal Control | Mathematics | Number Theory | Optimization | MATHEMATICS | COMPLEXIFICATIONS | REPRESENTATIONS | HOLOMORPHIC EXTENSIONS | GRAUERT TUBES | INVARIANT DOMAINS | STEIN EXTENSIONS | GEOMETRY

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2003, Volume 131, Issue 12, pp. 3839 - 3843

Let G=({\mathbb{R}},+) act by biholomorphisms on a taut manifold X. We show that X can be regarded as a G-invariant domain in a complex manifold X^{*} on which...

Mathematical manifolds | Riemann manifold | Algebra | Mathematical theorems | Globalization | Lie groups | Complexifications | Lie group actions | Taut and Stein manifolds | MATHEMATICS | MATHEMATICS, APPLIED | complexifications | SPACES | taut and Stein manifolds

Mathematical manifolds | Riemann manifold | Algebra | Mathematical theorems | Globalization | Lie groups | Complexifications | Lie group actions | Taut and Stein manifolds | MATHEMATICS | MATHEMATICS, APPLIED | complexifications | SPACES | taut and Stein manifolds

Journal Article

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