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Is there a way of constructing a morphism between Shimura varieties using differential equations? Maybe, this looks like a completely ridiculous question, so I think that I should explain the context of this question.

In this paper, three related ways of constructing a morphism of Shimura varieties (section 3.1-3.3) are introduced. Among them, the second construction uses realisations of monodromy groups of certain differential equations of second order with coefficients in $\mathbb{C}(z)$ and regular singularities at 0, 1, and $\infty$. I could not find any reference which explains the way of getting (or, finding) such differential equations. Again, I guess that this may be not enough for getting appropriate answer. I am really sorry for failing to ask well-posed question, but this is all I can do since I could not understand any relation between differential equation and Shimura varieties.

Anyone who can introduce related references will be really helpful. Thank you very much in advance.

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