On W-algebra extensions of (2,p) minimal models: p > 3

TL;DR

This paper extends the classification of irreducible representations from W_{2,3} to W_{2,p} for all odd p>3, revealing new logarithmic modules and analyzing the algebra's center structure.

Contribution

It generalizes the classification of irreducible modules to W_{2,p} for all odd p>3 and investigates the structure of the Zhu algebra's center.

Findings

Classification of irreducible modules for W_{2,p} extended to all odd p>3

Identification of logarithmic modules with specific L(0)-nilpotent ranks

Determination of the center structure of the Zhu algebra

Abstract

This is a continuation of arXiv:0908.4053, 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.