Consider a coxeter diagram $\Gamma$, i.e. a finite graph whose
edges are decorated by one of $\big\{3,4,6\big\}$. 
Let $p$ be a vertex of $\Gamma$ attached to a leaf $q$ and let
$m= m_{p,q}$ be the weight of the corresponding edge. Let $\mathring{\Gamma}$
be the induced coxeter diagram obtained by removing the leaf $q$.

Let $G$ and $\mathring{G}$ be the Kac-Moody groups associated to 
$\Gamma$ and $\mathring{\Gamma}$ respectively. Choose Borel 
subgroups $B$ and $\mathring{B}$ of $G$ and $\mathring{G}$ and let
$N$ and $\mathring{N}$ denote their associated unipotent radicals.

**Question:** Is there a representation $\mathcal{H}_{p,m}$ of $\mathring{N}$ such that
$N \cong \mathring{N} \rtimes \mathcal{H}_{p,m}$ ?