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Vertex Algebras W(p) ^{;; ; A_m};; ; and W(p) {;; ; D_m};; ; and Constant Term Identities

We consider AD-type orbifolds of the triplet vertex algebras W(p) extending the well-known c=1 orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras A(W(p)^{; ; ; A_m}; ; ; ) and A(W(p)^{; ; ; D_m}; ; ; ), where A_m and D_m are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible W(p)^Γ-modules is developed, which relies on a family of constant term identities and properties of certain polynomials based on constant terms. All these properties can be checked for small values of m and p with a computer software. As a result, we argue that if certain constant term properties hold, the irreducible modules constructed in [Commun. Contemp. Math. 15 (2013), 1350028, 30 pages, arXiv:1212.5453 ; Internat. J. Math. 25 (2014), 1450001, 34 pages, arXiv:1304.5711] provide a complete list of irreducible W(p)^{; ; ; A_m}; ; ; and W(p)^{; ; ; D_m}; ; ; -modules. This paper is a continuation of our previous work on the ADE subalgebras of the triplet vertex algebra W(p).

triplet vertex algebra ; orbifold subalgebra ; constant term identities.

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