Annihilating Fields of Standard Modules of $rak {sl}(2, Bbb {C})sim$ and Combinatorial Identities (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Hardcover

Meurman, Arne; Primc, Mirko

Hardcover

ISBN 10: 0821809237 ISBN 13: 9780821809235

Publisher: American Mathematical Society, 1999

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• Language: English
• ISBN 10: 0821809237
• ISBN 13: 9780821809235
• Binding: Hardcover
• Number of pages: 137