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.
Highlights
Letg be the affine Lie algebra associated with the finitedimensional simple Lie algebra g
Every highest-weightg-module of level k can be treated as a module for the vertex operator algebra (VOA) Nk(g)
We present a new explicit construction of singular vectors in Nk(g)
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 Adamovic (1994). 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 discussed.
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