Conformal Blocks, Generalized Theta Functions and the Verlinde Formula

Erscheinungsjahr 2021
ISBN: 978-1-316-51816-8
Verlag: Cambridge University Press

Buch, Englisch, Band 42, 540 Seiten, HC gerader Rücken kaschiert, Format (B × H): 157 mm x 235 mm, Gewicht: 1017 g

Reihe: New Mathematical Monographs

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.

Autoren/Hrsg.

Kumar, Shrawan

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Topologie

Inhaltsverzeichnis

Introduction; 1. An introduction to affine Lie algebras and the associated groups; 2. Space of vacua and its propagation; 3. Factorization theorem for space of vacua; 4. Fusion ring and explicit Verlinde formula; 5. Moduli stack of quasi-parabolic G-bundles and its uniformization; 6. Parabolic G-bundles and equivariant G-bundles; 7. Moduli space of semistable G-bundles over a smooth curve; 8. Identification of the space of conformal blocks with the space of generalized theta functions; 9. Picard group of moduli space of G-bundles; A. Dynkin index; B. C-space and C-group functors; C. Algebraic stacks; D. Rank-level duality (A brief survey) Swarnava Mukhopadhyay; Glossary; Bibliography; Index.

Über Autor(innen)

Kumar, Shrawan
Shrawan Kumar is John R. and Louise S. Parker Distinguished Professor of Mathematics at the University of North Carolina, Chapel Hill. He was an invited Speaker at the 2010 International Congress of Mathematicians and was elected a Fellow of the American Mathematical Society in 2012. This is his third book.