Softcover ISBN:  9781470410124 
Product Code:  CBMS/118 
List Price:  $69.00 
Individual Price:  $55.20 
eBook ISBN:  9781470414382 
Product Code:  CBMS/118.E 
List Price:  $69.00 
Softcover ISBN:  9781470410124 
eBook: ISBN:  9781470414382 
Product Code:  CBMS/118.B 
List Price:  $138.00 $103.50 
Softcover ISBN:  9781470410124 
Product Code:  CBMS/118 
List Price:  $69.00 
Individual Price:  $55.20 
eBook ISBN:  9781470414382 
Product Code:  CBMS/118.E 
List Price:  $69.00 
Softcover ISBN:  9781470410124 
eBook ISBN:  9781470414382 
Product Code:  CBMS/118.B 
List Price:  $138.00 $103.50 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 118; 2013; 308 ppMSC: Primary 14; 17; 22; 32; Secondary 20
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. Finitedimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinitedimensional 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 copublication of the AMS and CBMS.
ReadershipGraduate students and research mathematicians interested in complex geometry, Hodge theory, and representation theory.

Table of Contents

Chapters

1. Introduction

2. The classical theory: Part I

3. The classical theory: Part II

4. Polarized Hodge structures and MumfordTate groups and domains

5. Hodge representations and Hodge domains

6. Discrete series and $\mathfrak {n}$cohomology

7. Geometry of flag domains: Part I

8. Geometry of flag domains: Part II

9. Penrose transforms in the two main examples

10. Automorphic cohomology

11. Miscellaneous topics and some questions


Additional Material

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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. Finitedimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinitedimensional 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 copublication of the AMS and CBMS.
Graduate students and research mathematicians interested in complex geometry, Hodge theory, and representation theory.

Chapters

1. Introduction

2. The classical theory: Part I

3. The classical theory: Part II

4. Polarized Hodge structures and MumfordTate groups and domains

5. Hodge representations and Hodge domains

6. Discrete series and $\mathfrak {n}$cohomology

7. Geometry of flag domains: Part I

8. Geometry of flag domains: Part II

9. Penrose transforms in the two main examples

10. Automorphic cohomology

11. Miscellaneous topics and some questions