Original scientific paper

https://doi.org/10.3336/gm.48.1.07

A note on representations of some affine vertex algebras of type D

Ozren Perše ; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia

Abstract

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 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 LD4(-2,0). We also show that the maximal ideal in associated universal affine vertex algebra is generated by three singular vectors.

Keywords

Vertex operator algebra; affine Kac-Moody algebra; Zhu's algebra

Hrčak ID:

103274

URI

https://hrcak.srce.hr/103274

Publication date:

4.6.2013.

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