Let $G$ be a semisimple algebraic group over $\mathbb C$, $T$ be a maximal torus and $B$ be a Borel subgroup of $G$ containing $T$. Let $R^+$ be the set of positive roots with respect to $B$. Let $Q$ be a parabolic subgroup containing $B$ corresponding to a subset $\{\alpha_1, \alpha_2, \cdots ,\alpha_k \}$ of the set of simple roots $\{\alpha_1, \alpha_2, \cdots ,\alpha_n \}$.
Then Bruhat decomposition of $G/Q$ is given by $G/Q=\cup_{w \in W^Q}BwQ/Q$, where $W^Q$ is the Weyl group of $Q$.
$C_Q(w):=BwQ/Q$ is called a Schubert cell and its closure $X_w$ in $G/Q$ is called the Schubert variety associated to $w$. Let $B^-$ be the Borel subgroup of $G$ opposite to $B$. Then $B^-vQ/Q$ is called the opposite cell and its closure $X^v$ in $G/Q$ is called the opposite Schubert variety associated to $v$.
When $Q=B$ then $C_B(w)= \prod_{\{\alpha \in R^+: w^{-1}(\alpha) <0 \}}U_{\alpha}$, where $U_{\alpha}$ is the root subgroup corresponding to $\alpha$.
My questions are the following:
What is the expression for $C_Q(w)$ in terms of root subgroups for $Q \neq B$.
Let $v < w$ in Bruhat order. Then how does an element in $BwQ/Q \cap B^-vQ/Q$ look like in the form of a matrix.
Lets take $G=SL_6$, $B=$ the subgroup of upper triangular matrices and $Q$ be the maximal parabolic corresponding to the simple root $\alpha_2$, $w=s_2s_1s_5s_4s_3s_2$ and $v=s_3s_2$. If $x \in BwQ/Q \cap B^-vQ/Q$, then what is the matrix form of $x$ ?