Langlands Correspondence for Loop Groups (Relié)

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.