Timeline for A name for the Weyl group of $\frak{so_{2n}}$
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Aug 6 at 13:45 | vote | accept | Zoltan Fleishman | ||
| Aug 5 at 21:08 | answer | added | Steven Sam | timeline score: 10 | |
| Aug 5 at 13:48 | comment | added | LSpice | (I also take the opportunity to mention that my comment should have said that $W(\mathsf D_n)$ contains odd-as-unsigned permutations, not that it doesn't contain even-as-unsigned permutations. That is, my objection should have been that $W(\mathsf D_n) \cap W(\mathsf A_{n - 1})$ isn't the alternating subgroup of $W(\mathsf A_{n - 1})$, not that $W(\mathsf D_n)$ doesn't contain the alternating subgroup of $W(\mathsf A_{n - 1})$; of course the latter is false. @SamHopkins, thank you for reading my comment charitably as it was meant!) | |
| Aug 5 at 13:44 | history | edited | LSpice | CC BY-SA 4.0 |
Hopefully settling the wreath-product issue
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| Aug 5 at 10:36 | comment | added | Dave Benson | The first wreath now looks the wrong way round to me, and the second one just totally wrong because it's not even supposed to be a wreath product. | |
| Aug 5 at 10:31 | comment | added | მამუკა ჯიბლაძე | Maybe "special hyperoctahedral group"? | |
| S Aug 5 at 9:58 | history | suggested | Jules Lamers | CC BY-SA 4.0 |
Added second wreath product
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| Aug 5 at 0:14 | comment | added | Sam Hopkins | @LSpice Indeed I now see how that could be confusing. For example, in this paper doi.org/10.37236/1836 the terms "even-signed permutations" and "signed even permutations" are both used, which seems unnecessarily confusing to me. | |
| Aug 4 at 23:11 | comment | added | Zoltan Fleishman | Thanks a lot for the $\wr$ edits! | |
| Aug 4 at 22:25 | review | Suggested edits | |||
| S Aug 5 at 9:58 | |||||
| Aug 4 at 17:57 | comment | added | LSpice |
(By the way, the standard symbol for wreath product is \wr. I edited accordingly.)
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| Aug 4 at 17:56 | comment | added | LSpice | @SamHopkins, re, I'd argue that that terminology is a bit confusing since it sounds like it should include the even permutations, but doesn't. | |
| Aug 4 at 16:21 | comment | added | Sam Hopkins | @LSpice: on the other hand "group of even signed permutations" is totally clear and sounds fine, if a bit wordy. | |
| Aug 4 at 16:03 | comment | added | LSpice | Every Weyl group has a character that sends all reflections in long/short roots to $-1$, and reflections in short/long roots to $1$. (Which reflections are which depends on whether you call your root system $\mathsf C_n$ or $\mathsf B_n$.) If you call all roots of $\mathsf A_n$ long/short, then this is the sign homomorphism. From this point of view, I'd argue that $W(\mathsf D_n)$ is to the hyperoctahedral group as the alternating group is to $W(\mathsf A_n)$. I'd dare to suggest "alternating hyperoctahedral group", but (1) it's pretty terrible and (2) I've never seen it used. | |
| Aug 4 at 16:00 | history | edited | LSpice | CC BY-SA 4.0 |
Wreath product
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| Aug 4 at 15:50 | comment | added | Sam Hopkins | See en.wikipedia.org/wiki/Hyperoctahedral_group#Subgroups. I don't think there is any standard name for this group like "hyperoctahedral group" or "symmetric group." | |
| Aug 4 at 15:35 | history | asked | Zoltan Fleishman | CC BY-SA 4.0 |