Langlands Correspondence for Loop Groups

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Beschreibung

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.

Über den Autor

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

Zusammenfassung

Local geometric Langlands Correspondence is a new area of mathematical physics developed by the author and others in the last 20 years. The topic has many potential applications to Quantum Field Theory and String Theory. Based on courses taught at Berkeley, this text for advanced undergraduate students and graduate students, builds the theory from scratch, defines all necessary concepts and proves the essential results along the way. The author also provides many open problems which could form the basis for future research.

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2007
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
ISBN-13:	9780521854436
ISBN-10:	0521854431
Sprache:	Englisch
Einband:	Gebunden
Autor:	Frenkel, Edward
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	235 x 157 x 26 mm
Von/Mit:	Edward Frenkel
Erscheinungsdatum:	28.06.2007
Gewicht:	0,722 kg

Artikel-ID: 102089794

Über den Autor

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

Zusammenfassung

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2007
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
ISBN-13:	9780521854436
ISBN-10:	0521854431
Sprache:	Englisch
Einband:	Gebunden
Autor:	Frenkel, Edward
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	235 x 157 x 26 mm
Von/Mit:	Edward Frenkel
Erscheinungsdatum:	28.06.2007
Gewicht:	0,722 kg