ADE subalgebras of the triplet vertex algebra W(p): Dₘ-series

الأصل · EN

We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra W(p). This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex algebra M(1) +, the ₂--orbifold of the singlet vertex algebra M(1). Then we classify irreducible modules and determine Zhu's and C₂--algebra for the vertex algebra ᵈ². A general method for construction of twisted --modules is also introduced. We also discuss classification of twisted M(1)--modules including the twisted Zhu's algebra AΨ (M(1)), which is of independent interest. The category of admissible Ψ-twisted M(1)-modules is expected to be semisimple. We also prove C₂-cofiniteness of ᵈᵐ for all m, and give a conjectural list of irreducible ᵈᵐ-modules. Finally, we compute characters of the relevant irreducible modules and describe their modular closure.