**Contemporary Mathematics**

Volume: 46;
1985;
84 pp;
Softcover

MSC: Primary 17;

Print ISBN: 978-0-8218-5048-0

Product Code: CONM/46

List Price: $27.00

AMS Member Price: $21.60

MAA Member Price: $24.30

**Electronic ISBN: 978-0-8218-7631-2
Product Code: CONM/46.E**

List Price: $27.00

AMS Member Price: $21.60

MAA Member Price: $24.30

# Structure of the Standard Modules for the Affine Lie Algebra \(A^{(1)}_{1}\)

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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

## Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_{1}$

- Contents vii8 free
- Preface ix10 free
- 1. Introduction 112 free
- 2. The Lie algebra A1(1) 314
- 3. The category Pk 1021
- 4. The generalized commutation relations 1728
- 5. Relations for standard modules 2940
- 6. Basis of ΩL for a standard module L 3849
- 7. Schur functions 5061
- 8. Proof of linear independence 6778
- 9. Combinatorial formulas 7586
- References 8293