Let p be a prime. Given a split semisimple group scheme G over a normal integral domain R which is a faithfully flat $${\mathbb {Z}}_{(p)}$$ -algebra, we classify all finite dimensional representations V of the fiber $$G_K$$ of G over $$K:=Frac (R)$$ with the property that the set of lattices of V with respect to R which are G-modules is as well the set of lattices of V with respect to R which are $$Lie (G)$$ -modules. We apply this classification to get a general criterion of extensions of homomorphisms between reductive group schemes over $$Spec \,K$$ to homomorphisms between reductive group schemes over $$Spec \,R$$ . We also show that for a simply connected semisimple group scheme over a reduced $${\mathbb {Q}}$$ –algebra, the category of its representations is equivalent to the category of representations of its Lie algebra.