Glasnik matematički, Vol. 48 No. 1, 2013.
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
Publication date:
4.6.2013.
Visits: 971 *