An explicit realization of logarithmic modules for the vertex operator algebra W-p,W-p %26apos;

作者：Adamovic Drazen^*; Milas Antun

来源：Journal of Mathematical Physics, 2012, 53(7): 073511.

DOI：10.1063/1.4736424

By extending the methods used in our earlier work, in this paper, we present an explicit realization of logarithmic W-p,W-p%26apos;-modules that have L(0) nilpotent rank three. This was achieved by combining the techniques developed in [D. Adamovic and A. Milas, %26quot;Lattice construction of logarithmic modules for certain vertex algebras,%26quot; Selecta Math., New Ser. 15, 535-561 (2009); e-print arXiv:0902.3417] with the theory of local systems of vertex operators. [J. Lepowsky and H. Li, Introduction to Vertex Operator Algebras and Their Representations, Progress in Mathematics Vol. 227 (Birkhauser, Boston, 2003)] In addition, we also construct a new type of extension of W-p,W-p%26apos; denoted by V. Our results confirm several claims in the physics literature regarding the structure of projective covers of certain irreducible representations in the principal block. This approach can be applied to other models defined via a pair screenings.

• 出版日期2012-7