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Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities
Інший ID:
2010 Mathematics Subject Classification: 17B69
DOI:10.3842/SIGMA.2015.019
DOI:10.3842/SIGMA.2015.019
Посилання:
Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities / D. Adamović, X. Lin, A. Milas // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 15 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
We would like to thank the referees for their valuable comments. D.A. is partially supported by
the Croatian Science Foundation under the project 2634. X.L. is partially supported by National
Natural Science Foundation for young (no. 11401098). A.M. is partially supported by a Simons
Foundation grant.
Дата:
2015
Переглядів:
580
Завантажень:
341
Анотація:
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).
