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

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

2009-08-27

arxiv.org/abs/0908.4053v2

Mathematics

Quantum Algebra

27 pages, v2: minor changes

Scientific paper

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.

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