Hodge Theory, Complex Geometry, and Representation Theory
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A01=Mark Green
A01=Matt Kerr
A01=Phillip Griffiths
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Author_Mark Green
Author_Matt Kerr
Author_Phillip Griffiths
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Product details
- ISBN 9781470410124
- Weight: 545g
- Publication Date: 30 Dec 2013
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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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 realisation 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.
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.
Mark Green, University of California, Los Angeles, CA, USA
Phillip Griffiths, Institute of Advanced Study, Princeton, NJ, USA
Matt Kerr, Washington University, St. Louis, MO, USA
Phillip Griffiths, Institute of Advanced Study, Princeton, NJ, USA
Matt Kerr, Washington University, St. Louis, MO, USA
