Langlands Correspondence for Loop Groups

$114.00 (C)

Part of Cambridge Studies in Advanced Mathematics

Author: Edward Frenkel, University of California, Berkeley

Date Published: July 2007
availability: Available
format: Hardback
isbn: 9780521854436

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Description

The Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations, and has now expanded into such areas as Geometry and Quantum Field Theory, tying together seemingly unrelated disciplines into a web of tantalizing conjectures. A new chapter to this grand project is provided in this book. It develops the geometric Langlands Correspondence for Loop Groups, a new approach, from a unique perspective offered by affine Kac-Moody algebras. The theory offers fresh insights into the world of Langlands dualities, with many applications to Representation Theory of Infinite-dimensional Algebras, and Quantum Field Theory. This accessible text builds the theory from scratch, with all necessary concepts defined and the essential results proved along the way. Based on courses taught at Berkeley, the book provides many open problems which could form the basis for future research, and is accessible to advanced undergraduate students and beginning graduate students.
- The first account of local geometric Langlands Correspondence
- Suitable for advanced undergraduates and graduates in both mathematics and theoretical physics
- Contains many open problems which could form the basis for future research
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Reviews & endorsements
"This book provides and excellent detailed review of an important aspect of the geometric Langlands program, namely, the role of representation theory of affine Kac-Moody algebras (or loop algebras). It provides clear and insightful introductions to such notions as vertex algebras, the Langlands dual group, connections on the punctured disc, representation theory of loop algebras, etc., with many examples... a valuable resource for students and researchers in related fields.
David Ben-Zvi, Mathematical Reviews

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Product details
- Date Published: July 2007
- format: Hardback
- isbn: 9780521854436
- length: 396 pages
- dimensions: 235 x 160 x 25 mm
- weight: 0.681kg
- contains: 3 b/w illus. 1 table
- availability: Available
Table of Contents
Preface
1. Local Langlands Correspondence
2. Vertex algebras
3. Constructing central elements
4. Opers and the center for a general Lie algebra
5. Free field realization
6. Wakimoto modules
7. Intertwining operators
8. Identification of the center with functions on opers
9. Structure of bg-modules of critical level
10. Constructing the local Langlands Correspondence
Appendix
References.
Look Inside
Author
Edward Frenkel, University of California, Berkeley
Edward Frenkel is Professor of Mathematics at the University of California, Berkeley