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

Understand

For every odd p \geq 3, we investigate representation theory of the vertex algebra WW_{2,p} associated to (2,p) minimal models for the Virasoro algebras.

• We demonstrate that vertex algebras WW_{2,p} are C_2--cofinite and irrational.
• Complete classification of irreducible representations for WW_{2,3} is obtained, while the classification for p \geq 5 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.