Title: Annihilating Fields of Standard Modules of Sl(2, C) and Combinatorial Identities (Memoirs of the American Mathematical Society)
Publisher: Amer Mathematical Society
Publication Date: 1999
Language: English
ISBN 10: 0821809237
ISBN 13: 9780821809235
Binding: Hardcover
Condition: Good
Dust Jacket Condition: No Jacket
Weight: 0.44 pounds

About this title

Synopsis

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.

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