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Conformal Blocks, Generalized Theta Functions and the Verlinde Formula (Hardcover)
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Conformal Blocks, Generalized Theta Functions and the Verlinde Formula (Hardcover)
Series: New Mathematical Monographs
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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.
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