Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras
Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras
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DOI：
10.1142/8882
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
V. Kac;A. Raina;N. Rozhkovskaya
中科院分区：
文献类型：
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作者：
V. Kac;A. Raina;N. Rozhkovskaya
本书是V·卡茨教授1985年12月和1986年1月在印度塔塔研究所所做的一系列讲座的合集。这些讲座聚焦于最高权表示的概念，它有四种不同的形式。第一种是无限维海森堡代数（即振子代数）的正则对易关系。第二种是无限矩阵的李代数gl∞的最高权表示，以及它们在孤子方程理论中的应用，这是由佐藤以及伊达、吉姆博、柏原和三宅发现的。第三种是流（即仿射卡茨 - 穆迪）代数的酉最高权表示。这些代数在讲座中出现了两次，一次是在孤子方程的约化理论（KP→KdV）中，另一次是在菅原构造中，它是研究主要概念的第四种形式——维拉索罗代数的最高权表示理论的主要工具。
本书对数学家和物理学家都应该非常有用。对数学家来说，它阐明了无限维李代数表示理论的关键思想之间的相互作用；对物理学家来说，这一理论正在成为孤子理论、二维统计模型理论和弦理论等理论物理领域的重要组成部分。
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.