Talk:Parabolic subgroup of a reflection group

Parabolic subgroup of a reflection group is currently a Mathematics and mathematicians good article nominee. Nominated by JBL (talk) at 23:03, 1 September 2024 (UTC)

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Note: For purposes of criterion 1a ("understandable to an appropriately broad audience"): the high-quality sources that cover this topic are aimed at PhD students beginning to specialize or professional researchers in mathematics. In my opinion, this means that "an appropriately broad audience" should mean "advanced undergraduate mathematics majors and beginning PhD students in mathematics".

Things not in the article

It is obvious (given the information that is in the article) that the relation "is a standard parabolic subgroup of" is transitive on Coxeter groups, and not obvious but not difficult to prove that the relation "is a parabolic subgroup of" is transitive for complex reflection groups. In the references I consulted, I was not able to find a clear statement of these transitivities at this level of generality: Kane asserts it (on page 58) only for finite real reflection groups.

The question "why parabolic?" is very natural. The correct answer for reflection groups is "because of the connection with algebraic groups". The correct answer for algebraic groups is ... complicated. There's excellent discussion in this MathOverflow thread about it, but it does not produce a conclusive answer and is not citable anyhow.

JBL (talk) 19:38, 10 January 2024 (UTC)[reply]

I have added something about the name based on the MO thread. --JBL (talk) 22:00, 16 February 2024 (UTC)[reply]

Minor prose comment

This is not a big issue, but § Braid groups has a rather high density of parenthetical asides, enough to read a bit awkwardly to me. XOR'easter (talk) 22:27, 17 February 2024 (UTC)[reply]

@XOR'easter: yes indeed, thanks -- a chronic problem when I write quickly. (The section was thrown together as a sort of placeholder -- I will definitely revist it.) ( <-- illustrating the problem ;) ). --JBL (talk) 17:39, 18 February 2024 (UTC)[reply]

Well-written article

I'd just like to congratulate you on an extremely well-written and readable article. I personally can't understand a single word of it, of course. But I can somehow tell that if I'd taken a class in group theory instead of sticking to analysis, I'd definitely be able to read this and understand what it said. :p

(Or maybe not. I hate discrete math. Who TF put all these holes between my numbers‽) – Closed Limelike Curves (talk) 00:49, 19 September 2024 (UTC)[reply]

Sourcing issue

Hi @JayBeeEll: this is effectively the same thing as a listserv; we wouldn't consider professors emailing back and forth about research questions to be reliable, so we shouldn't consider them doing the same thing online for all to see reliable either. voorts (talk/contributions) 00:29, 28 October 2024 (UTC)[reply]

Hi voorts, sorry for the delayed response. At the level of what WP:GUNREL says, it's extremely clear: The source may still be used for uncontroversial self-descriptions, and self-published or user-generated content authored by established subject-matter experts is also acceptable. The linked page is a discussion between a number of subject-matter experts, in a scholarly (although unrefereed) venue; it definitely qualifies under the second half of the sentence I've quoted. (This description might also apply to some listservs, but that seems neither here nor there.) Personally I think the discussion there provides some small but very clear added value beyond what is found in Borel -- namely, the commentary of James E. Humphreys on what is found in Borel -- and that a reader interested in understanding this name is best served by being given both citations (even though there is no piece of information in the article here that relies on the MO thread). If you do not find this compelling, perhaps we can solicit a third opinion from WT:WPM? --JBL (talk) 00:28, 31 October 2024 (UTC)[reply]

No worries regarding the delay, and thank you for the response. I think that both references aren't needed per WP:BESTSOURCES and WP:TIERS, but your position on GUNREL is reasonable, so I'm fine with maintaining the status quo. Good luck with the GA nom. Best, voorts (talk/contributions) 02:17, 31 October 2024 (UTC)[reply]

I think you (plus the realization that I didn't include any content from the link, presumably because I was skeptical of reliability) have convinced me better out than in; for the record I preserve the citation here:

Chow, Timothy; et al. (2010), "Why are parabolic subgroups called "parabolic subgroups"?", MathOverflow, retrieved 2024-02-16

Thanks, JBL (talk) 00:36, 1 November 2024 (UTC)[reply]