**Memoirs of the American Mathematical Society**

1999;
89 pp;
Softcover

MSC: Primary 17;
Secondary 05

Print ISBN: 978-0-8218-0923-5

Product Code: MEMO/137/652

List Price: $49.00

AMS Member Price: $29.40

MAA Member Price: $44.10

**Electronic ISBN: 978-1-4704-0241-9
Product Code: MEMO/137/652.E**

List Price: $49.00

AMS Member Price: $29.40

MAA Member Price: $44.10

# Annihilating Fields of Standard Modules of \(\mathfrak{sl}(2, \mathbb{C})^{∼}\) and Combinatorial Identities

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*Arne Meurman; Mirko Primc*

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 Rogers-Ramanujan type combinatorial identities.

#### Readership

Graduate students and research mathematicians working in representation theory; theoretical physicists interested in conformal field theory.

#### Table of Contents

# Table of Contents

## Annihilating Fields of Standard Modules of $\mathfrak{sl}(2, \mathbb{C})^{}$ and Combinatorial Identities

- Contents vii8 free
- Abstract viii9 free
- Introduction 110 free
- 1. Formal Laurent series and rational functions 716 free
- 2. Generating fields 1322
- 3. The vertex operator algebra N(k[omitted]0) 2130
- 4. Modules over N(k[omitted]0) 2534
- 5. Relations on standard modules 3241
- 6. Colored partitions, leading terms and the main results 4049
- 7. Colored partitions allowing at least two embeddings 5362
- 8. Relations among relations 5867
- 9. Relations among relations for two embeddings 6271
- 10. Linear independence of bases of standard modules 7584
- 11. Some combinatorial identities of Rogers-Ramanujan type 8392
- Bibliography 8998