Timeline for action of symmetric group on the second exterior power
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2020 at 7:28 | comment | added | A. Gupta | For the action of $\langle (12)(34) \rangle$ there are six orbits only: $\{e_1 \wedge e_2, -e_1 \wedge e_2 \}$, $\{e_3 \wedge e_4, -e_3 \wedge e_4\}$, $\{e_1 \wedge e_3, e_2 \wedge e_4 \}$, $\{-e_1 \wedge e_3, -e_2 \wedge e_4 \}$, $\{e_1 \wedge e_4, e_2 \wedge e_3 \}$ and $\{-e_1 \wedge e_4, -e_2 \wedge e_3 \}$. The reason behind this is that $\langle (12) \rangle$ fixes more points in $\bar B$ (on average). | |
| May 1, 2020 at 7:12 | comment | added | A. Gupta | Please note: For $n = 4$ there are $7$ orbits for the group $\langle (12) \rangle$, namely, $\{\pm e_1\wedge e_2\}$, $\{e_1 \wedge e_3, e_2 \wedge e_3 \}$, $\{-e_1 \wedge e_3, -e_2 \wedge e_3 \}$, $\{e_1 \wedge e_4, e_2 \wedge e_4 \}$, $\{-e_1 \wedge e_4, -e_2 \wedge e_4 \}$, $\{e_3 \wedge e_4 \}$ and $-\{e_3 \wedge e_4\}$. | |
| Apr 30, 2020 at 17:22 | comment | added | Dan Petersen | The only exception is when $n=4$ in which case a product of two disjoint transposition also works. | |
| Apr 30, 2020 at 9:51 | vote | accept | A. Gupta | ||
| Apr 30, 2020 at 9:45 | history | edited | A. Gupta | CC BY-SA 4.0 |
deleted 13 characters in body
|
| Apr 30, 2020 at 7:23 | answer | added | Lior Silberman | timeline score: 2 | |
| Apr 30, 2020 at 6:16 | comment | added | A. Gupta | Yes, we mean exactly the restriction to $\bar B$ ("latter action" is now made explicit in the question). | |
| Apr 30, 2020 at 6:13 | history | edited | A. Gupta | CC BY-SA 4.0 |
added 21 characters in body
|
| Apr 30, 2020 at 5:51 | comment | added | A. Gupta | Please, note a modification in the question. | |
| Apr 30, 2020 at 5:49 | history | edited | A. Gupta | CC BY-SA 4.0 |
deleted 119 characters in body
|
| Apr 30, 2020 at 5:17 | history | edited | A. Gupta | CC BY-SA 4.0 |
added 236 characters in body
|
| Apr 30, 2020 at 3:59 | history | asked | A. Gupta | CC BY-SA 4.0 |