Orbit dimension formula
= Orbit dimension formula
{title2=$\dim\mathcal O_x=\dim G-\dim G_x$}
For an <algebraic group action>, the orbit dimension is the dimension of the group minus that of its stabilizer. For a finite-dimensional representation, the stabilizer is an automorphism group, open in its <endomorphism ring>, so their dimensions agree. In a <quiver representation space>, the <Ringel form> turns the orbit codimension into the dimension of the self-extension group.