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.
Publisher: Cambridge University Press
Number of pages: 396
Weight: 681 g
Dimensions: 235 x 160 x 25 mm
'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
"This book provides and excellent detailed review of an important aspect of the geometric Langlands program, namely, the role of representation theory of affine Kac-Moody algebras (or loop algebras). It provides clear and insightful introductions to such notions as vertex algebras, the Langlands dual group, connections on the punctured disc, representation theory of loop algebras, etc., with many examples... a valuable resource for students and researchers in related fields.
David Ben-Zvi, Mathematical Reviews