Conformal Blocks, Generalized Theta Functions and the Verlinde Formula

Download or read book Conformal Blocks, Generalized Theta Functions and the Verlinde Formula written by Shrawan Kumar and published by Cambridge University Press. This book was released on 2021-11-25 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics.