Electronic ISBN:  9781470402419 
Product Code:  MEMO/137/652.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $29.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 137; 1999; 89 ppMSC: Primary 17; Secondary 05;
In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra \(\tilde{\mathfrak g}\), they construct the corresponding level \(k\) vertex operator algebra and show that level \(k\) highest weight \(\tilde{\mathfrak g}\)modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level \(k\) standard modules and study the corresponding loop \(\tilde{\mathfrak g}\)module—the set of relations that defines standard modules. In the case when \(\tilde{\mathfrak g}\) is of type \(A^{(1)}_1\), they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of RogersRamanujan type combinatorial identities.
ReadershipGraduate students and research mathematicians working in representation theory; theoretical physicists interested in conformal field theory.

Table of Contents

Chapters

Introduction

1. Formal Laurent series and rational functions

2. Generating fields

3. The vertex operator algebra $N(k\Lambda _0)$

4. Modules over $N(k\Lambda _0)$

5. Relations on standard modules

6. Colored partitions, leading terms and the main results

7. Colored partitions allowing at least two embeddings

8. Relations among relations

9. Relations among relations for two embeddings

10. Linear independence of bases of standard modules

11. Some combinatorial identities of RogersRamanujan type


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In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra \(\tilde{\mathfrak g}\), they construct the corresponding level \(k\) vertex operator algebra and show that level \(k\) highest weight \(\tilde{\mathfrak g}\)modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level \(k\) standard modules and study the corresponding loop \(\tilde{\mathfrak g}\)module—the set of relations that defines standard modules. In the case when \(\tilde{\mathfrak g}\) is of type \(A^{(1)}_1\), they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of RogersRamanujan type combinatorial identities.
Graduate students and research mathematicians working in representation theory; theoretical physicists interested in conformal field theory.

Chapters

Introduction

1. Formal Laurent series and rational functions

2. Generating fields

3. The vertex operator algebra $N(k\Lambda _0)$

4. Modules over $N(k\Lambda _0)$

5. Relations on standard modules

6. Colored partitions, leading terms and the main results

7. Colored partitions allowing at least two embeddings

8. Relations among relations

9. Relations among relations for two embeddings

10. Linear independence of bases of standard modules

11. Some combinatorial identities of RogersRamanujan type