Langlands Correspondence for Loop Groups

Publié par Cambridge University Press, le 01 juillet 2007

379 pages

Résumé

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, weaving together seemingly unrelated disciplines into a web of tantalizing conjectures. This book provides a new chapter in this grand project. 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 introductory text builds the theory from scratch, with all necessary concepts defined and all essential results proved along the way.

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