engleski

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

We are continuing our investigation of ADE- orbifold subalgebras of the triplet vertex algebra W(p). This part deals with the dihedral series. First, we prove $C_2$-cofiniteness of $W(p) ^{; ; D_m}; ; $. Up to a certain constant term identity, we classify all irreducible modules for the vertex algebra $\overline{; ; M(1)}; ; ^+$, the $\Z_2$-- orbifold of the singlet vertex algebra $\overline{; ; M(1)}; ; $. We classify all irreducible modules and determine Zhu's and $C_2$--algebra for the vertex algebra $W(p)^{; ; D_2}; ; $. A general method for construction of twisted $W(p)$-- modules is also introduced.

vertex algebras; triplet vertex algebras; C_2 cofiniteness; Zhu's algebras; constant term identities

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