$\DeclareMathOperator\SL{SL}$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.