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ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA 𝒲(p): D-SERIES

DRAŽEN ADAMOVIĆ

Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia

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XIANZU LIN

College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350108, P. R. China

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, and

ANTUN MILAS

Department of Mathematics and Statistics, SUNY-Albany, 1400 Washington Avenue, Albany 12222, USA

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https://doi.org/10.1142/S0129167X14500013Cited by:8 (Source: Crossref)

Abstract

We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra 𝒲(p) initiated in D. Adamović, X. Lin and A. Milas, ADE subalgebras of the triplet vertex algebra 𝒲(p): A_m-series, Commun. Contemp. Math.15 (2013), Article ID: 1350028, 1–30. This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex algebra , the ℤ₂-orbifold of the singlet vertex algebra . Then, we classify irreducible modules and determine Zhu's and C₂-algebra for the vertex algebra 𝒲(p)^D₂. A general method for construction of twisted 𝒲(p)-modules is also introduced. We also discuss classification of twisted -modules including the twisted Zhu's algebra , which is of independent interest. The category of admissible Ψ-twisted -modules is expected to be semisimple. We also prove C₂-cofiniteness of 𝒲(p)^D_m for all m, and give a conjectural list of irreducible 𝒲(p)^D_m-modules. Finally, we compute characters of the relevant irreducible modules and describe their modular closure.

Keywords:

AMSC: 17B69, 17B67, 81R10

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