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Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$
 
Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$
Softcover ISBN:  978-0-8218-5048-0
Product Code:  CONM/46
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7631-2
Product Code:  CONM/46.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-5048-0
eBook: ISBN:  978-0-8218-7631-2
Product Code:  CONM/46.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
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 $A^{(1)}_1$
Softcover ISBN:  978-0-8218-5048-0
Product Code:  CONM/46
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7631-2
Product Code:  CONM/46.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-5048-0
eBook ISBN:  978-0-8218-7631-2
Product Code:  CONM/46.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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