All open cases of the Arakawa–Moreau maximal-ideal conjecture are proved: the prescribed singular vectors generate the maximal ideals at level -1 for D_l and at negative levels n>0 for D4, E6, E7, E8.
Representation Theory of Superconformal Algebras and the Kac–Roan–Wakimoto Conjecture.Duke Mathematical Journal130.3 (2005), 435–478
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Completing the Arakawa--Moreau Conjecture on Maximal Ideals of Affine Vertex Algebras
All open cases of the Arakawa–Moreau maximal-ideal conjecture are proved: the prescribed singular vectors generate the maximal ideals at level -1 for D_l and at negative levels n>0 for D4, E6, E7, E8.