Talk:Semisimple representation

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Montanabw^(talk) 17:11, 3 January 2020 (UTC)[reply]

• ... that how a spinning object influences the rotation of another spinning object in quantum mechanics is described by the structure of certain semisimple representations? Source: Clebsch–Gordan coefficients come from angular momentum coupling as evident from the WP article and its sources; the relation to semisimple representations comes from: "The representations of some semisimple and reductive Lie groups have become of increased importance in physics... to study CGCs of semisimple Lie groups." from Klimyk, A. U.; Gavrilik, A. M. (1979). "Representation matrix elements and Clebsch–Gordan coefficients of the semisimple Lie groups". Journal of Mathematical Physics. 20 (1624). doi:10.1063/1.524268.
  • ALT1:... that Clebsch–Gordan coefficients, which describe how spinning objects influence each other in quantum mechanics, come from the structure of semisimple representations? Source: same as above
  • ALT2:... that adding together two simple things might only make a semisimple one? Humor hook; Source: definition, e.g. Ch. 6, § 1.1, Definition 1 (ii) of Claudio Procesi (2007) Lie Groups: an approach through invariants and representation, Springer, ISBN 9780387260402.
  • ALT3:... that simple ⊕ simple = semisimple? Humor hook; Source: same as above; we could also use "+" instead of "⊕"

• Reviewed: Exempt - 4 DYKs

Created by TakuyaMurata (talk) and MarkH21 (talk). Nominated by MarkH21 (talk) at 12:46, 15 November 2019 (UTC).[reply]

• Comment (not a review): Don't the hidden-by-default proofs violate MOS:DONTHIDE "Collapsible templates should not conceal article content by default upon page loading"? —David Eppstein (talk) 02:03, 17 November 2019 (UTC)[reply]

• Ah, you’re right. Fixed and un-autocollapsed. — MarkH21 (talk) 02:11, 17 November 2019 (UTC)[reply]

• More not-really-reviewing: the entire "Examples and non-examples" section is unsourced. According to the DYK rules, every paragraph that is not merely a summary of later material (or plot summary of fiction) needs a source. —David Eppstein (talk) 01:41, 18 November 2019 (UTC)[reply]

• Pinging TakuyaMurata, did you have a source that we can cite for the non-example that you added? — MarkH21 (talk) 03:04, 18 November 2019 (UTC)[reply]

• I have added a few (not saying "enough"). -- Taku (talk) 23:40, 18 November 2019 (UTC)[reply]

• Full review needed. BlueMoonset (talk) 06:59, 24 November 2019‎ (UTC)[reply]

• On the day it was nominated, it was new enough and long enough. According to QPQ check, @TakuyaMurata: does not need a QPQ. Earwig is okay with it. Alt0 is the best hook IMHO, but it could be tightened up. I don't understand the math, so having a mathmetician look at it would be good. --evrik ^(talk) 21:50, 18 December 2019 (UTC)[reply]

• Requesting a second opinion on the math in the article. BlueMoonset (talk) 19:27, 20 December 2019 (UTC)[reply]

• I'll post a request for review in WikiProject Math because... there's a lot. Kingsif (talk) 17:16, 21 December 2019 (UTC)[reply]

• The math in the article looks correct. XOR'easter (talk) 21:37, 26 December 2019 (UTC)[reply]

• Thanks XOReaster - from previous reviews and this affirmation, I've looked at the article and all the current hooks look fine. I think Alt1 is easier to understand than alt0, but they're all fine. Kingsif (talk) 23:07, 26 December 2019 (UTC)[reply]

• I like alt1 a little more than alt0. XOR'easter (talk) 00:10, 27 December 2019 (UTC)[reply]

• @Kingsif: where does the article mention Clebsch–Gordan coefficients? Yoninah (talk) 23:07, 28 December 2019 (UTC)[reply]

• @Yoninah: From my understanding of the sources used for the first hooks, it's the sentence By Weyl's theorem on complete reducibility, every finite-dimensional representation of a semisimple Lie algebra over a field of characteristic zero is semisimple. Of course, neither Clebsch–Gordan coefficients nor angular momentum coupling are mentioned in the article, and I now see that the Klimyk/Gavrilik source isn't used in it to even support some complex mathematics that could be giving the same meaning. @MarkH21 and XOR'easter: to ask if the hook can be explicitly added to the article or something? Kingsif (talk) 23:31, 28 December 2019 (UTC)[reply]

• @Yoninah and Kingsif: That’s not a requirement for DYK to my understanding right? We certainly could add the sourced statement from the hook to the article, but then we would have to add a lot of other applications to the article though, since this would be undue prominence for Clebsch–Gordan coefficients. Semisimple representations are used all across physics! This is just one interesting application. — MarkH₂₁^talk 23:35, 28 December 2019 (UTC)[reply]

• @MarkH21: please read WP:DYK#Eligibility criteria 3. Cited hook. Yoninah (talk) 23:39, 28 December 2019 (UTC)[reply]

• @Yoninah: Ah my bad, I don't know why I assumed that it wasn't an explicit rule. Will add to the article with an "Applications" section soon. — MarkH₂₁^talk 23:42, 28 December 2019 (UTC)[reply]

• @Yoninah: Wasn't Alt0 cited? --evrik ^(talk) 20:05, 2 January 2020 (UTC)[reply]

• @Evrik: I didn't check. The reviewer preferred ALT1 for simplicity, and I agree, so that's the one I checked. Yoninah (talk) 21:24, 2 January 2020 (UTC)[reply]

• I would have passed this on December 18 if I had better understood the math. I am approving Alt0, as I believe it is sourced and ready to go. --evrik ^(talk) 21:35, 2 January 2020 (UTC)[reply]

• @Evrik and Yoninah: The source for ALT0 and ALT1 are the same, they're just minor variations of the same hook. I've added a basic "Applications" section to the article mentioning the fact in the hooks, this will be expanded in the future but should be sufficient for the DYK. — MarkH₂₁^talk 21:40, 2 January 2020 (UTC)[reply]

• @Evrik: thank you for your interest, but I was in the middle of a discussion with the nominator and I am not ready to sign off until I review his new edits. The ALT0 hook is too long and multisyllabic for comfortable reading and there's no reason to rush this off to the main page. I'm looking at MarkH21's work now. Yoninah (talk) 22:20, 2 January 2020 (UTC)[reply]

• Yoninah, FWIW I did the first review on this and I think I used this for QPQ credit. Just saying ... in any case I glad to see this move forward. --evrik ^(talk) 16:09, 3 January 2020 (UTC)[reply]

• Thank you, MarkH21. ALT1 is now sourced and the offline ref is AGF and cited inline. Rest of review per evrik and Kingsif. ALT1 good to go. Yoninah (talk) 22:27, 2 January 2020 (UTC)[reply]