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Topological groups. Lie groups --- Representations of groups --- Semisimple Lie groups --- Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Lie groups. --- Representations of groups. --- Représentations de groupes. --- Lie, Groupes de.
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512 --- Harmonic analysis --- -Representations of groups --- -Semisimple Lie groups --- -Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Algebra --- Congresses --- Semisimple Lie groups --- Representations of Lie groups --- -Algebra --- 512 Algebra --- -512 Algebra --- Semi-simple Lie groups --- Topological groups. Lie groups --- Harmonic analysis. Fourier analysis --- Analyse harmonique (mathématiques) --- Groupes de Lie semi-simples --- Représentations de groupes --- Representations of groups --- Représentations de groupes. --- Harmonic analysis - Congresses --- Semisimple Lie groups - Congresses --- Representations of Lie groups - Congresses --- Analyse harmonique (mathématiques) --- Représentations de groupes.
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Topological groups. Lie groups --- Representations of groups --- Semisimple Lie groups --- Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Semisimple Lie groups. --- Groupes de Lie semi-simples --- Représentations de groupes --- Groupes de Lie semi-simples. --- Représentations de groupes.
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Conjugacy classes --- Lie algebras --- Linear algebraic groups --- Semisimple Lie groups --- 512.74 --- 512.74 Algebraic groups. Abelian varieties --- Algebraic groups. Abelian varieties --- Semi-simple Lie groups --- Lie groups --- Algebraic groups, Linear --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Classes of conjugate elements
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Topological groups. Lie groups --- Semisimple Lie groups. --- Groupes de Lie semi-simples --- Representations of groups. --- Représentations de groupes --- Localization theory. --- Localisation, Théorie de la --- Localization theory --- Representations of groups --- Semisimple Lie groups --- Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Categories (Mathematics) --- Homotopy theory --- Nilpotent groups --- Groupes de Lie semi-simples. --- Représentations de groupes. --- Localisation, Théorie de la.
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Topological groups. Lie groups --- Differential geometry. Global analysis --- Complex manifolds --- Partially ordered spaces --- Semisimple Lie groups --- Flag manifolds --- 512 --- Flag varieties (Mathematics) --- Manifolds, Flag --- Varieties, Flag (Mathematics) --- Algebraic varieties --- Semi-simple Lie groups --- Lie groups --- Spaces, Partially ordered --- Ordered topological spaces --- Topological spaces --- Analytic spaces --- Manifolds (Mathematics) --- Algebra --- 512 Algebra --- Complex manifolds. --- Lie groups. --- Partially ordered spaces. --- Espaces partiellement ordonnés. --- Lie, Groupes de. --- Variétés complexes.
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This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.
Mathematics. --- Algebraic geometry. --- Associative rings. --- Rings (Algebra). --- Group theory. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Algebraic Geometry. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Algebraic geometry --- Geometry --- Math --- Science --- Geometry, Algebraic. --- Flag manifolds. --- Representations of groups. --- Semisimple Lie groups. --- Schubert varieties. --- MATHEMATICS -- Geometry -- General. --- Geometry, Algebraic --- Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Flag varieties (Mathematics) --- Manifolds, Flag --- Varieties, Flag (Mathematics) --- Algebraic varieties
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Algebra --- 51 <082.1> --- Mathematics--Series --- Semisimple Lie groups --- Linear algebraic groups --- Geometric group theory --- Lorentz groups --- Symmetric spaces --- Rings (Algebra) --- Groupes de Lie semi-simples --- Groupes algébriques linéaires --- Groupes, Théorie géométrique des --- Lorentz, Groupes de --- Espaces symétriques --- Anneaux (algèbre) --- Spaces, Symmetric --- Geometry, Differential --- Semi-simple Lie groups --- Lie groups --- Algebraic rings --- Ring theory --- Algebraic fields --- Algebraic groups, Linear --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- Groups, Lorentz --- Continuous groups --- Groupes de Lie semi-simples. --- Groupes algébriques linéaires. --- Groupes, Théorie géométrique des. --- Lorentz, Groupes de. --- Espaces symétriques.
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This monograph, divided into four parts, presents a comprehensive treatment and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry. Key features: * Accessible to readers from a wide range of fields, with all the necessary background material provided for the nonspecialist * Many new results presented for the first time * Driven by numerous examples * The exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and complex algebraic groups and their representations, as well as other areas of geometry * Comparisons with classical Barlet cycle spaces are given * Good bibliography and index Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work.
Semisimple Lie groups. --- Flag manifolds. --- Twistor theory. --- Automorphic forms. --- Homogeneous spaces. --- Spaces, Homogeneous --- Lie groups --- Automorphic functions --- Forms (Mathematics) --- Twistors --- Congruences (Geometry) --- Field theory (Physics) --- Space and time --- Flag varieties (Mathematics) --- Manifolds, Flag --- Varieties, Flag (Mathematics) --- Algebraic varieties --- Semi-simple Lie groups --- Global differential geometry. --- Topological Groups. --- Differential equations, partial. --- Global analysis. --- Geometry, algebraic. --- Quantum theory. --- Differential Geometry. --- Topological Groups, Lie Groups. --- Several Complex Variables and Analytic Spaces. --- Global Analysis and Analysis on Manifolds. --- Algebraic Geometry. --- Quantum Physics. --- Global analysis (Mathematics) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Algebraic geometry --- Geometry --- Partial differential equations --- Groups, Topological --- Continuous groups --- Geometry, Differential --- Differential geometry. --- Topological groups. --- Lie groups. --- Functions of complex variables. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Algebraic geometry. --- Quantum physics. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Topology --- Complex variables --- Elliptic functions --- Functions of real variables --- Differential geometry
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In this classic work, Anthony W. Knapp offers a survey of representation theory of semisimple Lie groups in a way that reflects the spirit of the subject and corresponds to the natural learning process. This book is a model of exposition and an invaluable resource for both graduate students and researchers. Although theorems are always stated precisely, many illustrative examples or classes of examples are given. To support this unique approach, the author includes for the reader a useful 300-item bibliography and an extensive section of notes.
Semisimple Lie groups. --- Representations of groups. --- Groupes de Lie semi-simples --- Représentations de groupes --- Semisimple Lie groups --- Representations of groups --- Semi-simple Lie groups --- Lie groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Représentations de groupes --- 512.547 --- 512.547 Linear representations of abstract groups. Group characters --- Linear representations of abstract groups. Group characters --- Abelian group. --- Admissible representation. --- Algebra homomorphism. --- Analytic function. --- Analytic proof. --- Associative algebra. --- Asymptotic expansion. --- Automorphic form. --- Automorphism. --- Bounded operator. --- Bounded set (topological vector space). --- Cartan subalgebra. --- Cartan subgroup. --- Category theory. --- Characterization (mathematics). --- Classification theorem. --- Cohomology. --- Complex conjugate representation. --- Complexification (Lie group). --- Complexification. --- Conjugate transpose. --- Continuous function (set theory). --- Degenerate bilinear form. --- Diagram (category theory). --- Dimension (vector space). --- Dirac operator. --- Discrete series representation. --- Distribution (mathematics). --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Existence theorem. --- Explicit formulae (L-function). --- Fourier inversion theorem. --- General linear group. --- Group homomorphism. --- Haar measure. --- Heine–Borel theorem. --- Hermitian matrix. --- Hilbert space. --- Holomorphic function. --- Hyperbolic function. --- Identity (mathematics). --- Induced representation. --- Infinitesimal character. --- Integration by parts. --- Invariant subspace. --- Invertible matrix. --- Irreducible representation. --- Jacobian matrix and determinant. --- K-finite. --- Levi decomposition. --- Lie algebra. --- Locally integrable function. --- Mathematical induction. --- Matrix coefficient. --- Matrix group. --- Maximal compact subgroup. --- Meromorphic function. --- Metric space. --- Nilpotent Lie algebra. --- Norm (mathematics). --- Parity (mathematics). --- Plancherel theorem. --- Projection (linear algebra). --- Quantifier (logic). --- Reductive group. --- Representation of a Lie group. --- Representation theory. --- Schwartz space. --- Semisimple Lie algebra. --- Set (mathematics). --- Sign (mathematics). --- Solvable Lie algebra. --- Special case. --- Special linear group. --- Special unitary group. --- Subgroup. --- Summation. --- Support (mathematics). --- Symmetric algebra. --- Symmetrization. --- Symplectic group. --- Tensor algebra. --- Tensor product. --- Theorem. --- Topological group. --- Topological space. --- Topological vector space. --- Unitary group. --- Unitary matrix. --- Unitary representation. --- Universal enveloping algebra. --- Variable (mathematics). --- Vector bundle. --- Weight (representation theory). --- Weyl character formula. --- Weyl group. --- Weyl's theorem. --- ZPP (complexity). --- Zorn's lemma.
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