$\DeclareMathOperator\SL{SL}$Let $F$ be a local field and $\mathcal{O}_{F}$ its valuation ring. Let $\pi\in \mathcal{O}_{F}$ be a uniformizer and $\mathfrak{p}=\pi\mathcal{O}_{F}$. Let $G$ be a split semisimple algebraic group over $F$. I think the case $G=\SL_{3}$ as an example. Let us consider a generator system $S=\{s_{1},s_{2},w_{1}\}$ of the affine Weyl group of $\SL_{3}(F)$, where
$$
s_{1}=
\left(
\begin{array}{ccc}
0 & 1 & 0 \\
-1 & 0 & 0 \\
0 & 0 & 1
\end{array}
\right),\quad
s_{2}=
\left(
\begin{array}{ccc}
1 & 0 & 0 \\
0 & 0 & 1 \\
0 & -1 & 0
\end{array}
\right),\quad
w_{1}=
\left(
\begin{array}{ccc}
0 & 0 & -\pi^{-1} \\
0 & 1 & 0 \\
\pi & 0 & 0
\end{array}
\right).
$$
It is well-known that holds the affine Bruhat decomposition $\SL_{3}(F)=B\langle S\rangle B$ and $\SL_{3}(\mathcal{O}_{F})=B\langle s_{1},s_{2}\rangle B$ where $B$ is the standard Iwahori subgroup of $\SL_{3}(F)$.

Question: What is the remaining component $B\langle w_{1}\rangle B=B\cup Bw_{1}B$? I want to know the explicit form of this subgroup.