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A construction of some ideals in affine vertex algebras

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  • Draen AdamoviĆ

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.

Suggested Citation

  • Draen AdamoviĆ, 2003. "A construction of some ideals in affine vertex algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:929385
    DOI: 10.1155/S0161171203201058
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