I am looking for the description of the centralizer $Z_G(X)$ , where $G$ is a real simple Lie Group and $X\in \ Lie (G) $ such that $X^d=0,\ X^{d-1}\neq 0 $. It is is helpful to me any references or any suggestion .

There is a unpublished manuscript by R. Proud, on the title “On centralizers of unipotent elements in algebraic groups”. If some one have a copy of this please post it.