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Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebra

Af: Ashok K Raina, Victor G Kac Engelsk Paperback

Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebra

Af: Ashok K Raina, Victor G Kac Engelsk Paperback
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This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. 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 gl∞ 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 algebras appear in the lectures twice, in the reduction theory of soliton equations (KP → KdV) and in the Sugawara construction as 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.

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 to physicists, this theory is turning into an important component of such domains of theoretical physics as soliton theory, theory of two-dimensional statistical models, and string theory.

 

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Tjek vores konkurrenters priser

This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. 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 gl∞ 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 algebras appear in the lectures twice, in the reduction theory of soliton equations (KP → KdV) and in the Sugawara construction as 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.

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 to physicists, this theory is turning into an important component of such domains of theoretical physics as soliton theory, theory of two-dimensional statistical models, and string theory.

 

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 160
ISBN-13: 9789971503963
Indbinding: Paperback
Udgave:
ISBN-10: 9971503964
Kategori: Algebra
Udg. Dato: 1 apr 1988
Længde: 10mm
Bredde: 154mm
Højde: 216mm
Forlag: EPB Publishers Pte Ltd
Oplagsdato: 1 apr 1988
Forfatter(e): Ashok K Raina, Victor G Kac
Forfatter(e) Ashok K Raina, Victor G Kac

Kategori Algebra

ISBN-13 9789971503963

Sprog Engelsk

Indbinding Paperback

Sider 160

Udgave

Længde 10mm

Bredde 154mm

Højde 216mm

Udg. Dato 1 apr 1988

Oplagsdato 1 apr 1988

Forlag EPB Publishers Pte Ltd