Over the years, I have heard two different proposed answers to this question.


1. It has something to do with parabolic elements of $SL(2,\mathbb{R})$. This sounds plausible, but I haven't heard a really convincing explanation along these lines.
2. "Parabolic" is short for "para-Borelic," meaning "containing a Borel subgroup."


Which answer, if either, is correct?


A related question is who first introduced the term and when. Chevalley perhaps?



Why are parabolic subgroups called "parabolic subgroups"?
It appears that neither of the answers is fully correct. There is a great book, "Essays in the history of Lie groups and algebraic groups" by Armand Borel, when it comes to references of this type. To quote from chapter VI section 2:



> 
> ...There was no nice terminology for the subgroups $P \_I$ with lie algebra the $\mathfrak p \_I$ until R. Godement suggested calling them parabolic subgroups. I shall therefore anachronistically call them that...
> 
> 
> 


"The geometry of the finite simple groups" by F. Buekenhout is on the other hand the only paper that came up in a search for paraborelic, and the author mentions he is using this term instead of parabolic to distinguish from parabolic subgroups of Chevalley groups.


