engleski

On W-algebra extensions of (2, p) Minimal Models: p > 3

This is a continuation of the paper [D. Adamovic, A. Milas, IMRN (2010) no. 20, 3896-3934], where, among other things, we classified irreducible representations of the triplet vertex algebra W_{; ; 2, 3}; ; . In this part we extend the classification to W_{; ; 2, p}; ; , for all odd p>3. We also determine the structure of the center of the Zhu algebra A(W_{; ; 2, p}; ; ) which implies the existence of a family of logarithmic modules having L(0)-nilpotent ranks 2 and 3. A logarithmic version of Macdonald-Morris constant term identity plays a key role in the paper.

Vertex algebras; W-algebras; Minimal models; Logarithmic conformal field theory

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