Langlands correspondence for loop groups


Langlands correspondence for loop groups

Edward Frenkel

(Cambridge studies in advanced mathematics, 103)

Cambridge University Press, 2007

  • : hardback

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Includes bibliographical references (p. 373-376) and index



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.


  • 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.

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  • ISBN
    • 9780521854436
  • 出版国コード
  • タイトル言語コード
  • 本文言語コード
  • 出版地
    Cambridge, UK
  • ページ数/冊数
    xvi, 379 p.
  • 大きさ
    24 cm
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