A construction of some ideals in affine vertex algebras
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 ex...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203201058 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |