Softcover ISBN:  9780821850480 
Product Code:  CONM/46 
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Electronic ISBN:  9780821876312 
Product Code:  CONM/46.E 
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Book DetailsContemporary MathematicsVolume: 46; 1985; 84 ppMSC: Primary 17;
The affine KacMoody algebra \(A_1^{(1)}\) has recently served as a source of new ideas in the representation theory of infinitedimensional 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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The affine KacMoody algebra \(A_1^{(1)}\) has recently served as a source of new ideas in the representation theory of infinitedimensional 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