• Reading Teleman

What's the input data? A compact Lie group (what's the difference between this and a complex reductive group?) and a polarisable quaternionic representation $E$ (ok, this is saying we can write $E =T^*V$, but we don't have a canonical choice of $V$, and we shouldn't fixiate on a choice.)

I don't know what's the difference between $g^{reg}/G$ and $g/G$ (adjoint action). OK, well, if we just do $g/G$, there might be too many orbits (with the same eigenvalues), and picking out $g^{reg}$ is saying, I am looking at the most generic (?) guy with this eigenvalues.