I'm trying to generalize a theorem on $SL_n(\mathbb Z)$$\operatorname{SL}_n(\mathbb Z)$ to the Chevalley groups over $\mathbb Z$.
In the theorem, there is a heavy use in the element $e_{1,n}(1)$ where
$$e_{1,n}(m)=
\begin{pmatrix}
1 & 0 & \cdots & m\\
& 1 & & \vdots\\
& & 1 & 0\\
& & & 1\\
\end{pmatrix}
$$$$e_{1,n}(m)=
\begin{pmatrix}
1 & 0 & \cdots & m\\
& 1 & & \vdots\\
& & 1 & 0\\
& & & 1\\
\end{pmatrix},
$$
together with a general element from the Bruhat big cell.
I
I was wanderingwondering if there is a way to charectizecharacterize $e_{1,n}(1)$ in the general Chevalley groups over $\mathbb Z$?