I used to think that things called "parabolic" must have something to do with parabolas or their defining quadratic equations. In fact, terms like parabolic coordinate, parabolic partial differential equation and so on, are indeed related to parabolas and their equations.
But, why are parabolic groups in algebraic group theory (correspondingly, parabolic subalgebras in Lie algebra theory) named "parabolic"? Do they have anything to do with parabolas or parabolic equations?
Thank you very much.