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Infinite Dimensional Lie Algebras : An Introduction

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Cover of 'Infinite Dimensional Lie Algebras : An Introduction'

Table of Contents

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    Book Overview
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    Chapter 1 Basic definitions
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    Chapter 2 The invariant bilinear form and the generalized Casimir operator
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    Chapter 3 Integrable representations and the Weyl group of a Kac-Moody algebra
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    Chapter 4 Some properties of generalized Cartan matrices
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    Chapter 5 Real and imaginary roots
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    Chapter 6 Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group
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    Chapter 7 Affine Lie algebras: the realization (case k=1)
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    Chapter 8 Affine Lie algebras: the realization (case k=2 or 3). Application to the classification of finite order automorphisms
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    Chapter 9 Highest weight modules over the Lie algebra g( A )
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    Chapter 10 Integrable highest weight modules: the character formula
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    Chapter 11 Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem
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    Chapter 12 Integrable highest weight modules over affine Lie algebras. Application to η -function identities
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    Chapter 13 Affine Lie algebras, theta functions and modular forms
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    Chapter 14 The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations
Attention for Chapter 2: The invariant bilinear form and the generalized Casimir operator
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Chapter title
The invariant bilinear form and the generalized Casimir operator
Chapter number 2
Book title
Infinite Dimensional Lie Algebras
Published by
Birkhäuser, Boston, MA, January 1983
DOI 10.1007/978-1-4757-1382-4_2
Book ISBNs
978-1-4757-1384-8, 978-1-4757-1382-4
Authors

Victor G. Kac, Kac, Victor G.

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