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Annihilating Fields of Standard Modules of SI(2, C) and Combinatorial Identities (Memoirs of the American Mathematical Society)

Annihilating Fields of Standard Modules of SI(2, C) and Combinatorial Identities (Memoirs of the American Mathematical Society)

By: Mirko Primc (author), Arne Meurman (author)Paperback

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Description

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.

Contents

Abstract Introduction Formal Laurent series and rational functions Generating fields The vertex operator algebra $N(k\Lambda 0)$ Modules over $N(k\Lambda 0)$ Relations on standard modules Colored partitions, leading terms and the main results Colored partitions allowing at least two embeddings Relations among relations Relations among relations for two embeddings Linear independence of bases of standard modules Some combinatorial identities of Rogers-Ramanujan type Bibliography.

Product Details

  • ISBN13: 9780821809235
  • Format: Paperback
  • Number Of Pages: 137
  • ID: 9780821809235
  • ISBN10: 0821809237

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