Timeline for Possible Borel subgroups of GL_n?
Current License: CC BY-SA 3.0
6 events
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| Nov 22, 2011 at 0:08 | comment | added | paul garrett | I think we (collectively) want both: the facile, possibly ad-hoc also tangible example/data-point, and the systematic reference to neo-classical literature. That is, examples are good, and over-arching concepts are good, and neither supplants the other. The pseudo-joke I tell my students about the definition of "parabolic" is its definition "G/P is complete", with the caveat that "complete" does not necessarily mean "projective", and so on. Yes, the classical projective imbeddings of Grassmannians and such are interesting, but I think it's ok to just give the example, too. Best to all... | |
| Nov 21, 2011 at 13:39 | comment | added | Jim Humphreys | @Tom: I don't mean to imply that the structure theory of reductive groups is itself easy or elementary, just that the question asked needs a systematic reference like Bourbaki rather than an ad hoc answer online. The Borel-Chevalley theory was an impressive development of Cartan's earlier work on Lie groups, while the 1965 IHES paper by Borel-Tits allowed arbitrary ground fields and was integrated with Bourbaki's axiomatization of root systems. Aside from that, the question needs more context: what sources dealing with Borel subgroups is the questioner starting from? | |
| Nov 21, 2011 at 5:00 | comment | added | Bruce Westbury | I agree with Jim. However I am not voting to close this question. | |
| Nov 21, 2011 at 2:18 | comment | added | Tom Church | With respect, there is no way this question is too elementary for this site. It is a reasonable question for a graduate student to ask -- or a research mathematician in another field, who might not know the standard references. I agree that the confusion is straightforward and easily cleared up, but I would say this shows that the question is the right amount of elementary for this site! | |
| Nov 21, 2011 at 0:16 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
added 117 characters in body
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| Nov 20, 2011 at 23:31 | history | answered | Jim Humphreys | CC BY-SA 3.0 |