Timeline for If you take a standard representation of a symmetric group, take an alternating tensor power of it, what groups appear as stabilizers of vectors?
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| Jul 2, 2010 at 12:09 | comment | added | rt-ist | Thanks for your reply. I agree with (1) but for (3) the situation is a bit more complicated. Write $e_{ijk} = e_i \wedge e_j \wedge e_k$. In $\Lambda^3 F^4$ (if char of $F$ is not 2) the stabilizer of $e_{123} + e_{124}$ is generated by $(3,4)$ and the stabilizer of $e_{234} + e_{134}$ is generated by $(1,2)$ but the stabilizer of $e_{123} + e_{124} - e_{234} - e_{134}$ is generated by $(1,3,4,2)$ which has nothing to do with the other two groups. | |
| Jul 2, 2010 at 4:41 | history | answered | zzl | CC BY-SA 2.5 |