A construction of some ideals in affine vertex algebras

Draen AdamoviĆ

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-10

Abstract:

We study ideals generated by singular vectors in vertex operator algebras associated with representations of affine Lie algebras of types A and C . We find new explicit formulas for singular vectors in these vertex operator algebras at integer and half-integer levels. These formulas generalize the expressions for singular vectors from Adamović (1994). As a consequence, we obtain a new family of vertex operator algebras for which we identify the associated Zhu's algebras. A connection with the representation theory of Weyl algebras is also discussed.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:929385

DOI: 10.1155/S0161171203201058

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