Base change action on quiver representations
= Base change action on quiver representations
{title2=$(g\cdot f)_\rho=g_{t(\rho)}f_\rho g_{s(\rho)}^{-1}$}
The group $\operatorname{GL}(\mathbf n)=\prod_i\operatorname{GL}_{n_i}(k)$ acts by $(g\cdot f)_\rho=g_{t(\rho)}f_\rho g_{s(\rho)}^{-1}$. Inverse entries are regular on a <general linear group>, so this is an <algebraic group action>. Its stabilizer is the <automorphism group of a quiver representation>.