An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'}

Details An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'} An explicit realization of logarithmic modules for the vertex operator algebra W_{p,p'}

2012-02-29

arxiv.org/abs/1202.6667v2

Mathematics

Quantum Algebra

18 pages, v2: one reference added, other minor changes

Scientific paper

By extending the methods used in our earlier work, in this paper, we present an explicit realization of logarithmic $\mathcal{W}_{p,p'$}-modules that have L(0) nilpotent rank three. This was achieved by combining the techniques developed in \cite{AdM-2009} with the theory of local systems of vertex operators \cite{LL}. In addition, we also construct a new type of extension of $\mathcal{W}_{p,p'}$, denoted by $\mathcal{V}$. 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.

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