On W-algebras associated to (2, p) minimal models and their representations

For every odd, we investigate the representation theory of the vertex algebra associated to (2, p) minimal models for the Virasoro algebras. We demonstrate that vertex algebras are C2 cofinite and irrational. Complete classification of irreducible representations for is obtained, while the classification for is subject to certain constant term identities. These identities can be viewed as "logarithmic deformations" of Dyson and Selberg constant term identities, and are of independent interest.