Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities

• Main Authors: Adamović, D., Lin, X., Milas, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/146992

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)Am) and A(W(p)Dm), where Am and Dm 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; Internat. J. Math. 25 (2014), 1450001, 34 pages] provide a complete list of irreducible W(p)Am and W(p)Dm-modules. This paper is a continuation of our previous work on the ADE subalgebras of the triplet vertex algebra W(p).