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2 produkter
2 produkter
Del 245 - Progress in Mathematics
Cycle Spaces of Flag Domains
A Complex Geometric Viewpoint
Inbunden, Engelska, 2005
1 413 kr
Skickas inom 10-15 vardagar
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, and their applications to harmonic analysis and algebraic geometry. Key features: All the necessary background material is provided for the nonspecialist, thus making the book accessible to readers from a wide range of fields. - The exposition, driven by numerous examples, is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also comes from real and complex algebraic groups and their representations as well as other areas of geometry. - Many new results presented for the first time - Comparisons with classical Barlet cycle spaces are given - Good bibliography and index Researchers and graduate students in complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, differential geometry and areas of global geometric analysis will benefit from this work.
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This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?ag domains. Some of the methods are now standard, but many are new. The exposition is carried out from the viewpoint of complex algebraic and differential geometry. Except for certain foundational material,whichisreadilyavailablefromstandardtexts,itisessentiallyself-contained; at points where this is not the case we give extensive references. After developing the background material on complex ?ag manifolds and rep- sentationtheory, wegiveanexposition(withanumberofnewresults)ofthecomplex geometric methods that lead to our characterizations of (group theoretically de?ned) cyclespacesandtoanumberofconsequences. Thenwegiveabriefindicationofjust how those results are related to the representation theory of semisimple Lie groups through, for example, the theory of double ?bration transforms, and we indicate the connection to the variation of Hodge structure. Finally, we work out detailed local descriptions of the relevant full Barlet cycle spaces. Cycle space theory is a basic chapter in complex analysis. Since the 1960s its importance has been underlined by its role in the geometry of ?ag domains, and by applications in the representation theory of semisimple Lie groups. This developed veryslowlyuntilafewofyearsagowhenmethodsofcomplexgeometry,inparticular those involving Schubert slices, Schubert domains, Iwasawa domains and suppo- ing hypersurfaces, were introduced. In the late 1990s, and continuing through early 2002, we developed those methods and used them to give a precise description of cycle spaces for ?ag domains. This effectively enabled the use of double ?bration transforms in all ?ag domain situations.