This question is for the algebraic groups. I find I cannot understand Levi decomposition for the parabolic subgroups well.
Denote the parabolic subgroup is P=LV, L is Levi subgroup. I guess that for the classical group, L is the diagonal element and the left part of it and V is right part of it with all the diagonal elements are 1.
Am I right? If yes, how to show it; if no, please give other interested examples.