A note on representations of some affine vertex algebras of type D
Abstract
In this note we construct a series of singular vectors in universal affine vertex operator algebras associated to
D
(1)
ℓ
of levels
n−ℓ+1
, for $n \in \Z_{>0}$. For
n=1
, we study the representation theory of the quotient vertex operator algebra modulo the ideal generated by that singular vector. In the case
ℓ=4
, we show that the adjoint module is the unique irreducible ordinary module for simple vertex operator algebra
L
D
4
(−2,0)
. We also show that the maximal ideal in associated universal affine vertex algebra is generated by three singular vectors.