Langlands correspondence for loop groups
Frenkel, Edward
Langlands correspondence for loop groups - Cambridge: Cambridge University Press, 2007. - xvi, 379 p. : ill. ; hb. ; 24 cm. - Cambridge studies in advanced mathematics ; Vol.103 .
Includes bibliographical references and index.
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.
9780521854436
Loops (Group theory)
Vertex algebras
Intertwining operators
Wakimoto modules
bg-modules
512.2 / FRE
Langlands correspondence for loop groups - Cambridge: Cambridge University Press, 2007. - xvi, 379 p. : ill. ; hb. ; 24 cm. - Cambridge studies in advanced mathematics ; Vol.103 .
Includes bibliographical references and index.
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.
9780521854436
Loops (Group theory)
Vertex algebras
Intertwining operators
Wakimoto modules
bg-modules
512.2 / FRE
