Timeline for Representations of finite groups over the "field with one element"
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2023 at 20:55 | comment | added | LSpice | The table of marks was also referenced in @SamHopkins's earlier comment. | |
| Apr 9, 2023 at 8:05 | comment | added | semisimpleton | Thanks! I'll take a look. | |
| Apr 9, 2023 at 8:05 | vote | accept | semisimpleton | ||
| Apr 9, 2023 at 6:50 | comment | added | Dave Benson | One can always argue about what is a "correct" analogy, but I'm really referring to the relationship between detection and induction. For details, please see Chapter 5 of "Representations and Cohomology, I". | |
| Apr 9, 2023 at 4:31 | comment | added | semisimpleton | @DaveBenson why are induced characters from cyclic subgroups the "correct" analogue of transitive permutation characters? I'm familiar with Artin's theorem on induced characters, but some of the rational coefficients in that theorem could well be negative, so while in a sense all characters are "made of" induced characters from cyclic subgroups, it doesn't seem very closely analogous to how every permutation character is a sum of transitive permutation characters. | |
| Apr 9, 2023 at 2:25 | comment | added | Timothy Chow | Is there some heuristic argument for why the table of marks "should" be thought of as the representation theory of finite groups over the field with one element? | |
| Apr 8, 2023 at 20:59 | comment | added | Gro-Tsen | @SamHopkins Another important difference | |
| Apr 8, 2023 at 19:42 | comment | added | Dave Benson | That's because the analogue in representation theory of the transitive permutation representations (induced from subgroups) isn't the basis of irreducible characters, but rather the induced characters from cyclic subgroups, as in Artin's induction theorem. | |
| Apr 8, 2023 at 19:34 | comment | added | Sam Hopkins | Though for an interesting way in which marks & character theory are dis-analogous, see: mathoverflow.net/questions/358037/… | |
| Apr 8, 2023 at 19:17 | history | answered | Dave Benson | CC BY-SA 4.0 |