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

Abstract

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.

27 pages, v2: minor changes

References in corpus (6)

• Logarithmic extensions of minimal models: characters and modular transformations
• Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
• Virasoro representations and fusion for general augmented minimal models
• Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I
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Cited by in corpus (3)

• A modular invariant bulk theory for the c=0 triplet model
• C_2-cofinite W-algebras and their logarithmic representations
• Fusion and (non)-rigidity of Virasoro Kac modules in logarithmic minimal models at $(p,q)$-central charge