Free product subgroups between Chevalley groups G(Φ,F) and G(Φ,F[t])

We investigate subgroups of a Chevalley group G=G(Φ,A) over a ring A, containing its elementary subgroup E=E(Φ,F) over a subring F⊆A. Assume that the root system Φ is simply laced and A=F[t] is a polynomial ring. We show that if G is of adjoint type, then there exists an element g∈E(Φ,A) such that 〈g,E(Φ,F)〉=〈g〉*E(Φ,F), where 〈X〉 denotes the subgroup, generated by a set X, and * stands for the free product.It follows that under the above assumptions the lattice L=L(E,G) is not standard. Moreover, combining the above result with theorems of Nuzhin and the author one obtains a necessary and sufficient condition for L to be standard provided that A and F are fields of characteristic not 2 and Φ≠G2.