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Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profound contributions to mathematics. Due to Professor Wolf’s broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume.  Algebraic, geometric, and analytic methods are employed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representation spaces are discussed. Contributions in the area of representation theory involve numerous viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis.   Contributors   D. Akhiezer                         T. Oshima A. Andrada                         I. Pacharoni M. L. Barberis                    F. Ricci L. Barchini                            S. Rosenberg I. Dotti                                  N. Shimeno M. Eastwood                     J. Tirao V. Fischer                            S. Treneer T. Kobayashi                       C.T.C. Wall A. Korányi                           D. Wallace B. Kostant                           K. Wiboonton P. Kostelec                          F. Xu K.-H. Neeb                          O. Yakimova G. Olafsson                         R. Zierau B. Ørsted.

Lie groups. --- Harmonic analysis. --- Linear topological spaces. --- Symmetric spaces. --- Wolf, Joseph Albert, --- Lie algebras. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Topological Groups. --- Algebra. --- Functional analysis. --- Topological Groups, Lie Groups. --- Associative Rings and Algebras. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Topological groups. --- Associative rings. --- Rings (Algebra). --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Wolf, Joseph A.

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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