God’s greatest creation?

I’m in California for 11 days, for (mostly) math.  Here’s something fun I just learned from Dick Gross.  Let G be a split simple algebraic group over \mathbf{Z}, and let V be (a \mathbf{Z}-lattice in) an irreducible algebraic representation of G.  It’s not hard to check that if V is minuscule, the representation V \otimes \mathbf{F}_p is an irreducible G \otimes \mathbf{F}_p-representation for every prime p.  Are there any other examples of V with this property?  It turns out there is exactly one more example: the adjoint representation of E_8.  When I said it was surprising to me that another such example existed, Dick explained that I shouldn’t be surprised, because after all, “E_8 is the greatest group that God ever created, so it’s not surprising that it has amazing properties like this”.

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