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