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Why do we ask Shimura datum to have Hodge weight $(-1,1),(0,0),(1,-1)$?

Why do we ask Shimura datum to have Hodge weight $(-1,1),(0,0),(1,-1)$? I know it's related to the decomposition of a complex Lie algebra $\frak{g}_{\mathbb{C}}=\frak{t}\oplus\frak{p}^{+} \oplus \frak ...
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