Timeline for Invariants of Symmetric group
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Mar 19, 2012 at 11:23 | vote | accept | mark | ||
| Mar 19, 2012 at 9:44 | vote | accept | mark | ||
| S Mar 19, 2012 at 11:23 | |||||
| Mar 18, 2012 at 22:52 | comment | added | Geoff Robinson | @Mariano: It's what was intended by the bracketed "this in particular tells you the precise representation" that was unclear to me. | |
| Mar 18, 2012 at 17:48 | comment | added | Mariano Suárez-Álvarez | @Geoff, well, it tells you what has to be checked! :D | |
| Mar 18, 2012 at 9:05 | vote | accept | mark | ||
| Mar 19, 2012 at 9:44 | |||||
| S Mar 18, 2012 at 9:04 | vote | accept | mark | ||
| Mar 18, 2012 at 9:05 | |||||
| Mar 18, 2012 at 9:04 | vote | accept | mark | ||
| S Mar 18, 2012 at 9:04 | |||||
| S Mar 18, 2012 at 9:04 | vote | accept | mark | ||
| Mar 18, 2012 at 9:04 | |||||
| Mar 18, 2012 at 9:04 | vote | accept | mark | ||
| S Mar 18, 2012 at 9:04 | |||||
| Mar 17, 2012 at 22:39 | comment | added | Jim Humphreys | @unknown: As Qiaochu points out, the first line of your question only invokes the fundamental theorem on symmetric functions for the symmetric group. The later general theorems due to Chevalley and Shephard-Todd apply to much more general finite groups and include "if and only if" statements relevant here (as others have pointed out). | |
| Mar 17, 2012 at 21:50 | comment | added | Geoff Robinson | @Mariano: This doesn't quite cover the question of whether $S_n$ acts as a reflection group is some other representation though, and in fact the realisation of $S_6$ as a reflection group in a non-standard way in $5$-dimension shows that there is something to check. | |
| Mar 17, 2012 at 19:27 | comment | added | macbeth | I'm glad this question was asked, since recently I too was interested in the more general first part (for what other representations of $S_n$ are generators [and relations] known explicitly?). Hope it gets answered! | |
| Mar 17, 2012 at 18:04 | answer | added | Geoff Robinson | timeline score: 10 | |
| Mar 17, 2012 at 17:56 | answer | added | Mark Wildon | timeline score: 17 | |
| Mar 17, 2012 at 16:44 | comment | added | Qiaochu Yuan | I know the theorem you state as the fundamental theorem of symmetric functions. Chevalley-Shephard-Todd is a more general theorem. | |
| Mar 17, 2012 at 16:12 | comment | added | Mariano Suárez-Álvarez | (See mathoverflow.net/questions/52457/…, which is relevant here) | |
| Mar 17, 2012 at 16:12 | comment | added | Mariano Suárez-Álvarez | It is a polynomial algebra exactly for the groups generated by pseudoreflections (this in particular tells you the precise representation) This is the full content of the C-S-T theorem. | |
| Mar 17, 2012 at 16:00 | history | edited | John Wiltshire-Gordon |
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| Mar 17, 2012 at 15:49 | history | asked | mark | CC BY-SA 3.0 |