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

Arne Meurman University of Lund, Lund, Sweden
Mirko Primc University of Zagreb, Zagreb, Croatia
Available Formats:
Electronic ISBN: 978-1-4704-0241-9
Product Code: MEMO/137/652.E
89 pp
List Price: $49.00 MAA Member Price:$44.10
AMS Member Price: $29.40 Click above image for expanded view Annihilating Fields of Standard Modules of$\mathfrak {sl}(2, \mathbb {C})^\sim$and Combinatorial Identities Arne Meurman University of Lund, Lund, Sweden Mirko Primc University of Zagreb, Zagreb, Croatia Available Formats:  Electronic ISBN: 978-1-4704-0241-9 Product Code: MEMO/137/652.E 89 pp  List Price:$49.00 MAA Member Price: $44.10 AMS Member Price:$29.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 1371999
MSC: 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 Rogers-Ramanujan 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 Rogers-Ramanujan type
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Volume: 1371999
MSC: 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 Rogers-Ramanujan 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 Rogers-Ramanujan type
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