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Langlands Correspondence for Loop Groups

Autor Edward Frenkel
en Limba Engleză Hardback – 27 iun 2007
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.
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Specificații

ISBN-13: 9780521854436
ISBN-10: 0521854431
Pagini: 396
Ilustrații: 3 b/w illus. 1 table
Dimensiuni: 160 x 235 x 25 mm
Greutate: 0.67 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

'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

Notă biografică


Descriere

The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.