Glasnik Matematicki, Vol. 48, No. 1 (2013), 81-90.

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

Ozren Perše

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: perse@math.hr


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.

2010 Mathematics Subject Classification.   17B69, 17B67, 81R10.

Key words and phrases.   Vertex operator algebra, affine Kac-Moody algebra, Zhu's algebra.


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DOI: 10.3336/gm.48.1.07


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