Conformal Blocks, Generalized Theta Functions and the Verlinde Formula

E. Verlinde's conjectural formula for the dimension of conformal blocks over a smooth curve is discussed in this book, which provides a proof of the formula and its connection to generalized theta functions. It is of interest to senior graduate students and researchers in geometry, representation theory, and theoretical physics.

Format: Hardback
Length: 540 pages
Publication date: 25 November 2021
Publisher: Cambridge University Press

In 1988, E. Verlinde presented a groundbreaking conjectural formula for the dimension of conformal blocks over a smooth curve, which was later interpreted as the space of generalized theta functions. This formula, derived from physical considerations, gained significant attention from mathematicians when it was realized that it could be understood through the study of representations of affine Lie algebras. Over the years, numerous mathematicians contributed to the proof of Verlinde's formula, culminating in its comprehensive validation in the 1990s.

This book serves as an authoritative resource on the subject, offering a thorough proof of the Verlinde formula and providing comprehensive insights into its connection with generalized theta functions. It includes detailed explanations of the construction of relevant moduli spaces and stacks of G-bundles, making it an invaluable tool for senior graduate students and researchers in geometry, representation theory, and theoretical physics.

The book is organized into well-structured chapters, each accompanied by exercises of varying difficulty. Additionally, it includes comprehensive guides to the broader literature and concise appendices on essential concepts, ensuring a comprehensive understanding of the theory. Whether you are a seasoned expert or a newcomer to the field, this book will provide you with valuable insights and serve as a valuable reference for your research endeavors.

Weight: 948g
Dimension: 159 x 236 x 40 (mm)
ISBN-13: 9781316518168