TY - BOOK ID - 210314 TI - Cycle spaces of flag domains : a complex geometric viewpoint AU - Fels, Gregor. AU - Huckleberry, Alan T. AU - Wolf, J. A. PY - 2006 SN - 1280611278 9786610611270 0817644792 0817643915 PB - Boston : Birkhauser, DB - UniCat KW - Semisimple Lie groups. KW - Flag manifolds. KW - Twistor theory. KW - Automorphic forms. KW - Homogeneous spaces. KW - Spaces, Homogeneous KW - Lie groups KW - Automorphic functions KW - Forms (Mathematics) KW - Twistors KW - Congruences (Geometry) KW - Field theory (Physics) KW - Space and time KW - Flag varieties (Mathematics) KW - Manifolds, Flag KW - Varieties, Flag (Mathematics) KW - Algebraic varieties KW - Semi-simple Lie groups KW - Global differential geometry. KW - Topological Groups. KW - Differential equations, partial. KW - Global analysis. KW - Geometry, algebraic. KW - Quantum theory. KW - Differential Geometry. KW - Topological Groups, Lie Groups. KW - Several Complex Variables and Analytic Spaces. KW - Global Analysis and Analysis on Manifolds. KW - Algebraic Geometry. KW - Quantum Physics. KW - Global analysis (Mathematics) KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Quantum dynamics KW - Quantum mechanics KW - Quantum physics KW - Physics KW - Mechanics KW - Thermodynamics KW - Algebraic geometry KW - Geometry KW - Partial differential equations KW - Groups, Topological KW - Continuous groups KW - Geometry, Differential KW - Differential geometry. KW - Topological groups. KW - Lie groups. KW - Functions of complex variables. KW - Global analysis (Mathematics). KW - Manifolds (Mathematics). KW - Algebraic geometry. KW - Quantum physics. KW - Groups, Lie KW - Lie algebras KW - Symmetric spaces KW - Topological groups KW - Topology KW - Complex variables KW - Elliptic functions KW - Functions of real variables KW - Differential geometry UR - https://www.unicat.be/uniCat?func=search&query=sysid:210314 AB - 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. ER -