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Let G be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field F of characteristic p >= 0, and let u is an element of G be a non-identity unipotent element. Let phi be a non-trivial irreducible representation of G. Then the Jordan normal form of phi(u) contains at most one non-trivial block if and only if G is of type G(2), u is a regular unipotent element and dim phi
Donna Testerman, Martin W. Liebeck