# Annihilating fields of standard modules of ${\germ s}{\germ l}(2,{\bf C})^\sim $ and combinatorial identities

### About this Title

**Arne Meurman** and **Mirko Primc**

Publication: Memoirs of the American Mathematical Society

Publication Year
1999: Volume 137, Number 652

ISBNs: 978-0-8218-0923-5 (print); 978-1-4704-0241-9 (online)

DOI: http://dx.doi.org/10.1090/memo/0652

MathSciNet review: 1458529

MSC: Primary 17B69; Secondary 05A19, 17B67

### 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 Rogers-Ramanujan type