## 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”.