A construction of some ideals in affine vertex algebras
Abstract
Let $N_{k} (\g)$ be a vertex operator algebra (VOA) associated to the generalized Verma module for affine Lie algebra of type $A_{\ell 1} ^{(1)}$ or $C_{\ell} ^{(1)}$. We construct a family of ideals $J_{m,n} (\g)$ in $N_{k} (\g)$, and a family $V_{m,n} (\g)$ of quotient VOAs. These families include VOAs associated to the integrable representations, and VOAs associated to admissible representations at halfinteger levels investigated in qalg/9502015. We also explicitly identify the Zhu's algebras $A(V_{m,n} (\g))$ and find a connection between these Zhu's algebras and Weyl algebras.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:math/0103006
 Bibcode:
 2001math......3006A
 Keywords:

 Quantum Algebra;
 17B69;
 17B67
 EPrint:
 10 pages, Latex, minor changes