Timeline for Can the intersection of a maximal parabolic with a closed sub-group contain more than one maximal parabolic?

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Dec 9, 2011 at 14:17	comment	added	Keerthi Madapusi		Thanks for that last example. I think the issue there is that the intersection of $P_2$ with $G_1$ is all of $G_1$. So, as long as we exclude that possibility, the answer to my last question should be 'yes', I think.
Dec 9, 2011 at 13:54	comment	added	Jim Humphreys		@Keerthi: I'm not yet sure I've understood what your precise questions are, but there seem to be positive and negative answers even in the case of split groups. I've added another type of example, since you allow Borel subgroups to be viewed as minimal parabolics.
Dec 9, 2011 at 13:53	history	edited	Jim Humphreys	CC BY-SA 3.0	added 70 characters in body
Dec 9, 2011 at 13:22	history	edited	Jim Humphreys	CC BY-SA 3.0	added 540 characters in body
Dec 8, 2011 at 22:46	comment	added	Keerthi Madapusi		And yes all sub-groups are defined over $\mathbb{Q}$.
Dec 8, 2011 at 22:44	comment	added	Keerthi Madapusi		Sorry, I realize now that it wasn't so clear, but what I wanted to know is that the situations in my first two questions never happen. This would of course follow from an affirmative answer to my last question. And George McNinch is right, 'minimal' is Borel inclusive, but 'maximal' is 'maximal proper'.
Dec 8, 2011 at 20:50	comment	added	George McNinch		I suspect that the term "minimal parabolic" is in this case not supposed to rule out a Borel. Since the OP wants to work over $\mathbf{Q}$, in general $G_1$ needn't have a Borel defined over $\mathbf{Q}$, but one can speak of a "minimal $\mathbf{Q}$-parabolic".
Dec 8, 2011 at 20:30	history	edited	Jim Humphreys	CC BY-SA 3.0	added 647 characters in body
Dec 8, 2011 at 18:49	history	answered	Jim Humphreys	CC BY-SA 3.0