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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
Front Cover for Annihilating Fields of Standard Modules of sl(2, C)^~  and Combinatorial Identities
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
Front Cover for Annihilating Fields of Standard Modules of sl(2, C)^~  and Combinatorial Identities
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  • Front Cover for Annihilating Fields of Standard Modules of sl(2, C)^~  and Combinatorial Identities
  • Back Cover for Annihilating Fields of Standard Modules of sl(2, C)^~  and Combinatorial Identities
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.

    Readership

    Graduate 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 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.

Readership

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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