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

This is a continuation of Adamović and Milas (2010) [5], where, among other things, we classified irreducible representations of the triplet vertex algebra W2,3. In this part we extend the classification to W2,p, for all odd p>3. We also determine the structure of the center of the Zhu algebra A(W2,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.