**CBMS Regional Conference Series in Mathematics**

Volume: 118;
2013;
308 pp;
Softcover

MSC: Primary 14; 17; 22; 32;
Secondary 20; 53

Print ISBN: 978-1-4704-1012-4

Product Code: CBMS/118

List Price: $65.00

Individual Price: $52.00

**Electronic ISBN: 978-1-4704-1438-2
Product Code: CBMS/118.E**

List Price: $65.00

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#### Supplemental Materials

# Hodge Theory, Complex Geometry, and Representation Theory

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*Mark Green; Phillip Griffiths; Matt Kerr*

A co-publication of the AMS and CBMS

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.

#### Table of Contents

# Table of Contents

## Hodge Theory, Complex Geometry, and Representation Theory

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Introduction 16 free
- The classical theory: Part I 510 free
- The classical theory: Part II 1722
- Polarized Hodge structures and Mumford-Tate groups and domains 3136
- Hodge representations and Hodge domains 5156
- Discrete series and 𝔫 6974
- Geometry of flag domains: Part I 95100
- Geometry of flag domains: Part II 147152
- Penrose transforms in the two main examples 165170
- Automorphic cohomology 191196
- Miscellaneous topics and some questions 221226
- Bibliography 299304
- Index 303308 free
- Notations used in the talks 307312
- Back Cover Back Cover1314

#### Readership

Graduate students and research mathematicians interested in complex geometry, Hodge theory, and representation theory.