Hodge Theory, Complex Geometry, and Representation Theory

Hodge Theory, Complex Geometry, and Representation Theory (Regional Conference Series in Mathematics)

This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.
Country USA
Manufacturer American Mathematical Society
Binding Paperback
ItemPartNumber illustrations
UnitCount 1
EANs 9781470410124
ReleaseDate 0000-00-00

Country	USA
Manufacturer	American Mathematical Society
Binding	Paperback
ItemPartNumber	illustrations
UnitCount	1
EANs	9781470410124
ReleaseDate	0000-00-00

Hodge Theory, Complex Geometry, and Representation Theory (Regional Conference Series in Mathematics)

You might also like...