 Quiver representation space

At fixed dimension vector, ${\mathrm{Rep}}_Q(\mathbf{n})={\prod }_{\rho :i\to j}{\mathrm{Hom}}_k(k^{n_i},k^{n_j})$ is an irreducible affine space of dimension ${\sum }_{\rho }{n}_{s(\rho )}{n}_{t(\rho )}$. Its points are arrow-matrix collections, and its base-change orbits are isomorphism classes.