Langlands Correspondence for Loop Groups

Focusing on the geometric Langlands Correspondence for Loop Groups, this book presents a fresh approach utilizing affine Kac-Moody algebras. It connects Number Theory, Automorphic Representations, Geometry, and Quantum Field Theory, revealing new insights into Langlands dualities and their applications in Representation Theory of Infinite-dimensional Algebras. Written for advanced undergraduates and beginning graduate students, it builds the theory from the ground up, defining concepts and proving essential results, while also presenting open problems for future research.