International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 15, Pages 971-980
doi:10.1155/S0161171203201058

A construction of some ideals in affine vertex algebras

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.