$Q$ are in bijection with the set of positive roots $R^+$ of the root system corresponding to the underlying Dynkin diagram. Fix an ordering $R^+=\{\beta_1,\beta_2,\dotsc,\beta_N\}$ of the set of positive roots and write $I_j$ for the (isomorphism class of an) indecomposable representation of $Q$ corresponding to $\beta_j$. The correspondence $I_j \leftrightarrow \beta_j$ is determined as follows: the dimension vector of the indecomposable $I_j$ is given by the expansion $\beta_j = \sum_{i\in Q_0} \dim I_j(i) \, \alpha_i$ of the corresponding positive root $\beta_j$ in the basis $\{\alpha_i\mid i\in Q_0\}$ of simple roots.

Thus there is a bijection between the $GL$-orbits in ${\mathrm{Hom}}={\mathrm{Hom}}(Q,d)$ and the direct sums $\bigoplus_{j=1}^N I_j^{\,\oplus m_j}$ where $(m_j\mid j = 1,\ldots,N)$ satisfies the obvious dimension condition $$\begin{aligned}
 \label{E:dim}
  \text{for all $i\in Q_0$},\quad
  d(i) = \sum_{j=1}^N d_j(i), \qquad\text{where }
  \ d_j(i) := m_j \dim(I_j(i)).\end{aligned}$$ Fix such a tuple of multiplicities $m = (m_j)$ and let $\Omega_m
\subset {\mathrm{Hom}}$ be the closure of the corresponding $GL$-orbit.

Based on $m$ we define a parabolic $P_m\subset GL$ and a linear subspace $Z_m\subset{\mathrm{Hom}}$ as follows. For each vertex $i\in Q_0$ we divide the sets of row and column indices of $GL({\mathbb{C}}^{d(i)})$ into contiguous subsets of sizes $d_j(i)$ as $j$ runs from $1$ to 