My question is simple:
Given an algebraic group $G$ acting on a variety $X$ algebraically. If the orbits are of finite number then they form what is called an algebraic stratification of $X$.
Now my question is: Is this (the stratification by $G$-orbits) also a Whitney Stratification?
I think showing this by hand is quite painfull since the definition of a Whitney stratification is very unhandy.
I would appreciate any reference.