Timeline for Representations of finite groups over the "field with one element"
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 9, 2023 at 12:20 | comment | added | Andrew | Weyl groups, including the symmetric groups, are often viewed as the corresponding algebraic group over a field with one element. See, for example, mathoverflow.net/questions/272498/… and en.wikipedia.org/wiki/Weyl_group. | |
| Apr 9, 2023 at 8:05 | vote | accept | semisimpleton | ||
| Apr 8, 2023 at 23:40 | history | became hot network question | |||
| Apr 8, 2023 at 19:17 | answer | added | Dave Benson | timeline score: 16 | |
| Apr 8, 2023 at 16:57 | comment | added | Sam Hopkins | I'll let somebody more knowledgeable answer that question about applications of the Burnside ring. Certainly there has been significant work on it since Burnside. My impression is that it is less "tractable" than the representation ring; as is usual in mathematics, linearizing makes life easier. | |
| Apr 8, 2023 at 16:17 | comment | added | semisimpleton | Thanks! Has the study of the Burnside ring been important in answering more down-to-earth questions about finite group actions, just as ordinary character theory has been useful in answering "purely" group-theoretic questions? | |
| Apr 8, 2023 at 15:53 | comment | added | Sam Hopkins | There already is an analog of character tables for permutation representation called the "table of marks," going back > 100 years to work of Burnside: en.wikipedia.org/wiki/Burnside_ring#Marks | |
| S Apr 8, 2023 at 15:40 | review | First questions | |||
| Apr 8, 2023 at 15:42 | |||||
| S Apr 8, 2023 at 15:40 | history | asked | semisimpleton | CC BY-SA 4.0 |