A NOTE ON REPRESENTATIONS OF SOME AFFINE VERTEX ALGEBRAS OF TYPE D

In this note we construct a series of singular vectors in universal affine vertex operator algebras associated to D-l((1)) of levels n-l + 1, for n is an element of 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-D4 (-2, 0). We also show that the maximal ideal in associated universal affine vertex algebra is generated by three singular vectors.