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A realization for a $\mathbb{Q}$-Hermitian variation of Hodge structure of Calabi-Yau type with real multiplication
We show that the Q-descents of the canonical R-variation of Hodge structure of Calabi-Yau type over a tube domain of type A can be realized as sub-variations of Hodge structure of certain Q-variations of Hodge structure which are naturally associated to abelian varieties of (generalized) Weil type.