Weil classes on every abelian sixfold of Weil type for $\mathbb{Q}(\sqrt{-3})$
We prove that the Weil classes of every polarized complex abelian sixfold of Weil type for $K=\mathbb{Q}(\sqrt{-3})$, of every Hermitian discriminant, are algebraic. The same holds for every abelian eightfold of Weil type for $K$ of signature $(4,4)$ with split discriminant, and every power of such a sixfold whose special Mumford--Tate group is $SU_H$ satisfies the Hodge conjecture. The proof applies the transfer theorem of the companion preprint to the Shephard--Todd group $G_{34}$ with twenty reflections as local monodromies, and passes from eightfolds to sixfolds by a compensation…
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