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Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras (2nd Edition) (Paperback, 2nd Revised ed.)
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Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras (2nd Edition) (Paperback, 2nd Revised ed.)
Series: Advanced Series In Mathematical Physics, 29
Expected to ship within 10 - 15 working days
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The first edition of this book is a collection of a series of
lectures given by Professor Victor Kac at the TIFR, Mumbai, India
in December 1985 and January 1986. These lectures focus on the idea
of a highest weight representation, which goes through four
different incarnations.The first is the canonical commutation
relations of the infinite dimensional Heisenberg Algebra (=
oscillator algebra). The second is the highest weight
representations of the Lie algebra g of infinite matrices, along
with their applications to the theory of soliton equations,
discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third
is the unitary highest weight representations of the current (=
affine Kac-Moody) algebras. These Lie algebras appear in the
lectures in connection to the Sugawara construction, which is the
main tool in the study of the fourth incarnation of the main idea,
the theory of the highest weight representations of the Virasoro
algebra. In particular, the book provides a complete proof of the
Kac determinant formula, the key result in representation theory of
the Virasoro algebra.The second edition of this book incorporates,
as its first part, the largely unchanged text of the first edition,
while its second part is the collection of lectures on vertex
algebras, delivered by Professor Kac at the TIFR in January 2003.
The basic idea of these lectures was to demonstrate how the key
notions of the theory of vertex algebras - such as quantum fields,
their normal ordered product and lambda-bracket, energy-momentum
field and conformal weight, untwisted and twisted representations -
simplify and clarify the constructions of the first edition of the
book.This book should be very useful for both mathematicians and
physicists. To mathematicians, it illustrates the interaction of
the key ideas of the representation theory of infinite dimensional
Lie algebras and of the theory of vertex algebras; and to
physicists, these theories are turning into an important component
of such domains of theoretical physics as soliton theory, conformal
field theory, the theory of two-dimensional statistical models, and
string theory.
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