Conformal Blocks, Generalized Theta Functions and the Verlinde Formula
Published on 25. November 2021
Book
Hardback
538 pages
978-1-316-51816-8 (ISBN)
Description
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.
Reviews / Votes
'The author succeeds in giving a masterful, clear, motivated and practically up to date presentation of a subject which is connected to the forefront of the mathematical research. It is addressed both to those researchers who just enter the subject and to those already active in theoretical physics, algebraic geometry, representation theory. This admirable book (which is the third book of Shrawan Kumar) is the first one about a very advanced and technical subject and it will be surely a standard reference.' Nicolae Manolache, zbMATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 36 mm
Weight
1015 gr
ISBN-13
978-1-316-51816-8 (9781316518168)
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Schweitzer Classification
Other editions
Additional editions
E-Book
12/2021
Cambridge University Press
€127.99
Available for download
Person
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.
Content
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.