Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras.pdf

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras PDF

Victor G. Kac

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 1= oscillator algebra).The second is the highest weight representations of the Lie algebra gecoof 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 Kay-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 theTIFR 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

Bombay Lectures On Highest Weight …

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Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras.pdf

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Sofya Voigtuh

Bombay Lectures on Highest Weight … 01/04/1988 · System Upgrade on Feb 12th During this period, E-commerce and registration of new users may not be available for up to 12 hours. For online purchase, please visit us again.

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Mattio Müllers

Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebra by Victor G. Kac, 9789971503963, available at Book Depository with free delivery worldwide.

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Noels Schulzen

∞-dimensional Lie algebra, omnipresent in 2-dimensional conformal ... Ashok K. Raina, and Natasha Rozhkovskaya, Bombay lectures on highest weight representations of infinite dimensional Lie algebras, second ed., Advanced Series in ... 2 Feb 2011 ... underlying finite dimensional Lie algebra. ... highest weight representation of an affine Kac-Moody group can be described by a family of ... Kac, V. G., Raina, A. K. : Bombay lectures on highest weight representations of infinite.

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Jason Leghmann

Bombay lectures on highest weight representations of infinite dimensional lie algebras. Raina, A. K. Singapore: World Scientific. ISBN 9971503956. OCLC 18475755. CS1 maint: numeric names: authors list ; Kac, Victor (1997). Vertex Algebras for Beginners (University Lecture Series, No 10). American Mathematical Society. ISBN 0-8218-0643-2.

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Jessica Kolhmann

Bombay Lectures on Highest Weight … 01/08/2014 · Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras, 2nd Edition Victor G. Kac, Ashok K. Raina, and Natasha Rozhkovskaya World Scientific 2013 237 pages $38.00 Advanced Series in Mathematical Physics; Volume 29 QA252