Vertex Algebras [...] and [...] and Constant Term Identities

• Published in: Symmetry, integrability and geometry, methods and applications Vol. 11
• Main Authors: Adamovic, Drazen, Lin, Xianzu, Milas, Antun
• Format: Journal Article
• Language: English
• Published: Kiev National Academy of Sciences of Ukraine 01.01.2015
• ISSN: 1815-0659
• DOI: 10.3842/SIGMA.2015.019

We consider [...]-type orbifolds of the triplet vertex algebras [...] extending the well-known [...] orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras [...] and [...], where [...] and [...] are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible [...]-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 [...] and [...] 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 [...] and [...]-modules. This paper is a continuation of our previous work on the [...] subalgebras of the triplet vertex algebra [...]. [ProQuest: [...] denotes formulae omitted.]