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Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$
 
Front Cover for Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$
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Softcover ISBN: 978-0-8218-5048-0
Product Code: CONM/46
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AMS Member Price: $23.20
Electronic ISBN: 978-0-8218-7631-2
Product Code: CONM/46.E
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Front Cover for Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$
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Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$
Available Formats:
Softcover ISBN:  978-0-8218-5048-0
Product Code:  CONM/46
List Price: $29.00
MAA Member Price: $26.10
AMS Member Price: $23.20
Electronic ISBN:  978-0-8218-7631-2
Product Code:  CONM/46.E
List Price: $27.00
MAA Member Price: $24.30
AMS Member Price: $21.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $43.50
MAA Member Price: $39.15
AMS Member Price: $34.80
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 461985; 84 pp
    MSC: Primary 17;

    The affine Kac-Moody algebra \(A_1^{(1)}\) has recently served as a source of new ideas in the representation theory of infinite-dimensional affine Lie algebras. In particular, several years ago it was discovered that \(A_1^{(1)}\) and then a general class of affine Lie algebras could be constructed using operators related to the vertex operators of the physicists' string model. This book develops the calculus of vertex operators to solve the problem of constructing all the standard \(A_1^{(1)}\)-modules in the homogeneous realization.

    Aimed primarily at researchers in and students of Lie theory, the book's detailed and concrete exposition makes it accessible and illuminating even to relative newcomers to the field.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. The Lie algebra $A_1^{(1)}$
    • 3. The category $\mathcal {P}_k$
    • 4. The generalized commutation relations
    • 5. Relations for standard modules
    • 6. Basis of $\Omega _L$ for a standard module $L$
    • 7. Schur functions
    • 8. Proof of linear independence
    • 9. Combinatorial formulas
    • References
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Volume: 461985; 84 pp
MSC: Primary 17;

The affine Kac-Moody algebra \(A_1^{(1)}\) has recently served as a source of new ideas in the representation theory of infinite-dimensional affine Lie algebras. In particular, several years ago it was discovered that \(A_1^{(1)}\) and then a general class of affine Lie algebras could be constructed using operators related to the vertex operators of the physicists' string model. This book develops the calculus of vertex operators to solve the problem of constructing all the standard \(A_1^{(1)}\)-modules in the homogeneous realization.

Aimed primarily at researchers in and students of Lie theory, the book's detailed and concrete exposition makes it accessible and illuminating even to relative newcomers to the field.

  • Chapters
  • 1. Introduction
  • 2. The Lie algebra $A_1^{(1)}$
  • 3. The category $\mathcal {P}_k$
  • 4. The generalized commutation relations
  • 5. Relations for standard modules
  • 6. Basis of $\Omega _L$ for a standard module $L$
  • 7. Schur functions
  • 8. Proof of linear independence
  • 9. Combinatorial formulas
  • References
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