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.



Algebraic Stratifications of $G$-varieties
So Ulrich and Geordie were right, Tom Braden was the right person to ask and here is what he told me:


The answer is yes, in the case above $X$ is Whitney stratified.


The argument goes roughly as follows. In the paper [K] the following is shown. Let $X$ be an algebraic stratified variety and $ S$ a stratum. The set $Sing(S )$ of points in $S $ which do not fulfil Whitney's b condition has the structure of a (semi-)variety of dimension strictly lower that $\dim S $. 


Now applied to our situation :
$Sing(S)$ is necessarly $G$-invariant, hence empty. This answers my question. 


[K] ``A Geometric Proof of Existence of Whitney Stratifications’’, Moscow Math. Journ., 5 (2005), no.1, 125—133


