| eBook ISBN: | 978-1-4704-0241-9 |
| Product Code: | MEMO/137/652.E |
| List Price: | $49.00 |
| MAA Member Price: | $44.10 |
| AMS Member Price: | $29.40 |
| eBook ISBN: | 978-1-4704-0241-9 |
| Product Code: | MEMO/137/652.E |
| List Price: | $49.00 |
| MAA Member Price: | $44.10 |
| AMS Member Price: | $29.40 |
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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 Rogers-Ramanujan type combinatorial identities.
ReadershipGraduate students and research mathematicians working in representation theory; theoretical physicists interested in conformal field theory.
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Table of Contents
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Chapters
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Introduction
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1. Formal Laurent series and rational functions
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2. Generating fields
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3. The vertex operator algebra $N(k\Lambda _0)$
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4. Modules over $N(k\Lambda _0)$
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5. Relations on standard modules
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6. Colored partitions, leading terms and the main results
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7. Colored partitions allowing at least two embeddings
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8. Relations among relations
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9. Relations among relations for two embeddings
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10. Linear independence of bases of standard modules
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11. Some combinatorial identities of Rogers-Ramanujan 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 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
