Langlands Correspondence for Loop Groups

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Hardcover | 28 June 2007

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396 Pages

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22.86 x 15.24 x 2.24

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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.

Industry Reviews

'This book is well written and will give especially the interested student, an excellent basis in this rapidly developing area of mathematics. For those beyond the level of student it also provides very useful text to follow, and perhaps to participate, in these developments.' Samuel James Patterson, Zentralblatt MATH

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Preface
Local Langlands Correspondence
Vertex algebras
Constructing central elements
Opers and the center for a general Lie algebra
Free field realization
Wakimoto modules
Intertwining operators
Identification of the center with functions on opers
Structure of bg-modules of critical level
Constructing the local Langlands Correspondence
Appendix
References
Table of Contents provided by Publisher. All Rights Reserved.

Langlands Correspondence for Loop Groups

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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