Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Hodge Theory, Complex Geometry, and Representation Theory
 
Mark Green University of California, Los Angeles, Los Angeles, CA
Phillip Griffiths Institute of Advanced Study, Princeton, NJ
Matt Kerr Washington University, St. Louis, MO
A co-publication of the AMS and CBMS
Hodge Theory, Complex Geometry, and Representation Theory
Softcover ISBN:  978-1-4704-1012-4
Product Code:  CBMS/118
List Price: $69.00
Individual Price: $55.20
eBook ISBN:  978-1-4704-1438-2
Product Code:  CBMS/118.E
List Price: $69.00
Softcover ISBN:  978-1-4704-1012-4
eBook: ISBN:  978-1-4704-1438-2
Product Code:  CBMS/118.B
List Price: $138.00 $103.50
Hodge Theory, Complex Geometry, and Representation Theory
Click above image for expanded view
Hodge Theory, Complex Geometry, and Representation Theory
Mark Green University of California, Los Angeles, Los Angeles, CA
Phillip Griffiths Institute of Advanced Study, Princeton, NJ
Matt Kerr Washington University, St. Louis, MO
A co-publication of the AMS and CBMS
Softcover ISBN:  978-1-4704-1012-4
Product Code:  CBMS/118
List Price: $69.00
Individual Price: $55.20
eBook ISBN:  978-1-4704-1438-2
Product Code:  CBMS/118.E
List Price: $69.00
Softcover ISBN:  978-1-4704-1012-4
eBook ISBN:  978-1-4704-1438-2
Product Code:  CBMS/118.B
List Price: $138.00 $103.50
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 1182013; 308 pp
    MSC: 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. 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.

    Readership

    Graduate 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 Mumford-Tate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1182013; 308 pp
MSC: 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. 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.

Readership

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 Mumford-Tate 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.