Title: ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA š¯’²(p): D-SERIES
Abstract:We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra š¯’²(p) initiated in D. Adamović, X. Lin and A. Milas, ADE subalgebras of the triplet vertex algebra š¯’²(p): A m -serie...We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra š¯’²(p) initiated in D. Adamović, X. Lin and A. Milas, ADE subalgebras of the triplet vertex algebra š¯’²(p): A m -series, Commun. Contemp. Math.15 (2013), Article ID: 1350028, 1ā€“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 [Formula: see text], the ā„¤ 2 -orbifold of the singlet vertex algebra [Formula: see text]. Then, we classify irreducible modules and determine Zhu's and C 2 -algebra for the vertex algebra š¯’²(p) D 2 . A general method for construction of twisted š¯’²(p)-modules is also introduced. We also discuss classification of twisted [Formula: see text]-modules including the twisted Zhu's algebra [Formula: see text], which is of independent interest. The category of admissible ĪØ-twisted [Formula: see text]-modules is expected to be semisimple. We also prove C 2 -cofiniteness of š¯’²(p) D m for all m, and give a conjectural list of irreducible š¯’²(p) D m -modules. Finally, we compute characters of the relevant irreducible modules and describe their modular closure.Read More
Publication Year: 2014
Publication Date: 2014-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 11
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