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For every odd, we investigate the representation theory of the vertex algebraassociated to (2,  p ) minimal models for the Virasoro algebras. We demonstrate that vertex algebrasare  C  2  cofinite and irrational. Complete classification of irreducible representations foris obtained, while the classification foris 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.

On W-Algebras Associated to (2, p ) Minimal Models and Their Representations