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Langlands Correspondence for Loop Groups

Langlands Correspondence for Loop Groups

£74.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: June 2007
  • availability: In stock
  • format: Hardback
  • isbn: 9780521854436

£ 74.99
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About the Authors
  • 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 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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    Product details

    • Date Published: June 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: In stock
  • 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.

  • Author

    Edward Frenkel, University of California, Berkeley
    Edward Frenkel is Professor of Mathematics at the University of California, Berkeley

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