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The two-character level-1 WZW models corresponding to Lie algebras in theCvitanovi\'c-Deligne series $A_1,A_2,G_2,D_4,F_4,E_6,E_7$ have been argued toform coset pairs with respect to the meromorphic $E_{8,1}$ CFT. Evidence forthis has taken the form of holomorphic bilinear relations between thecharacters. We propose that suitable 4-point functions of primaries in thesemodels also obey bilinear relations that combine them into current correlatorsfor $E_{8,1}$, and provide strong evidence that these relations hold in eachcase. Different cases work out due to special identities involving tensorinvariants of the algebra or hypergeometric functions. In particular theseresults verify previous calculations of correlators for exceptional WZW models,which have rather subtle features. We also find evidence that the intermediatevertex operator algebras A$_{0.5}$ and E$_{7.5}$, as well as thethree-character A$_{4,1}$ theory, also appear to satisfy the novel cosetrelation.

Universal Correlators and Novel Cosets in 2d RCFT