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
Department of Mathematics, University of Zagreb, Bijenička 30, Zagreb 10 000, Croatia
Received 15 January 2002
Copyright © 2003 Dražen AdamoviĆ. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.