Annihilating Fields of Standard Modules of Sl(2, C) and Combinatorial Identities (Memoirs of the American Mathematical Society) by Arne Meurman (PDF)

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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.

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