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    Langlands Correspondence for Loop Groups (Cambridge Studies in Advanced Mathematics (Hardcover)) (Hardback) By (author) Edward Frenkel

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    DescriptionThe 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.


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  • Full bibliographic data for Langlands Correspondence for Loop Groups

    Title
    Langlands Correspondence for Loop Groups
    Authors and contributors
    By (author) Edward Frenkel
    Physical properties
    Format: Hardback
    Number of pages: 396
    Width: 158 mm
    Height: 230 mm
    Thickness: 26 mm
    Weight: 680 g
    Language
    English
    ISBN
    ISBN 13: 9780521854436
    ISBN 10: 0521854431
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    B&T Modifier: Region of Publication: 03
    B&T General Subject: 710
    B&T Modifier: Continuations: 02
    BIC subject category V2: PBM
    B&T Modifier: Academic Level: 02
    LC classification: QA
    Ingram Subject Code: MA
    Libri: I-MA
    BIC subject category V2: PBP
    Warengruppen-Systematik des deutschen Buchhandels: 16240
    BISAC V2.8: MAT002000
    B&T Merchandise Category: UP
    BIC subject category V2: PHU, PBG
    DC22: 512.2
    LC subject heading:
    Thema V1.0: PBG
    Illustrations note
    3 b/w illus. 1 table
    Publisher
    CAMBRIDGE UNIVERSITY PRESS
    Imprint name
    CAMBRIDGE UNIVERSITY PRESS
    Publication date
    30 July 2007
    Publication City/Country
    Cambridge
    Author Information
    Edward Frenkel is Professor of Mathematics at the University of California, Berkeley
    Review quote
    '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
    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.