Hodge theory, complex geometry, and representation theory
Author(s)
Bibliographic Information
Hodge theory, complex geometry, and representation theory
（Regional conference series in mathematics, no. 118）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c2013
Available at / 36 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
"With support from the National Science Foundation"
"NSF/CBMS Regional Conference in Mathematical Sciences : Hodge Theory, Complex Geometry, and Representation Theory held at Texas Christian University, Fort Worth, Texas, June 18-22, 2012"--T.p. verso
Bibliography: p. 299-302
Includes index
Description and Table of Contents
Description
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.
Table of Contents
Introduction
The classical theory: Part I
The classical theory: Part II
Polarized Hodge structures and Mumford-Tate groups and domains
Hodge representations and Hodge domains
Discrete series and 𝔫
Geometry of flag domains: Part I
Geometry of flag domains: Part II
Penrose transforms in the two main examples
Automorphic cohomology
Miscellaneous topics and some questions
Bibliography
Index
by "Nielsen BookData"