Timeline for semisimple restricted representation
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 5, 2011 at 11:36 | comment | added | Jim Humphreys | @sife: Your last question needs a more precise formulation concerning the indices of the subgroups relative to the given prime number. Like the original question asked, this further question seems too loose to answer directly. | |
| Jun 5, 2011 at 11:32 | answer | added | Jim Humphreys | timeline score: 2 | |
| Jun 5, 2011 at 10:45 | comment | added | sife | Yes. But my question is that: if the restricted representation $V|_{H}$ is semisimple, in what conditions can we deduce that $V$ is semisimple? Here $H$ need not be a normal subgroup. Furthermore, we consider several restricted representations $\{V|_{H_{i}}\}$. If the restricted representations $\{V|_{H_{i}}\}$ are semisimple, in what conditions can we deduce that $V$ is semisimple? | |
| Jun 5, 2011 at 8:04 | comment | added | Niels | It is probably obvious to you, but I think it is should be mentioned that the other way round, you have Clifford's theorem in modular representation theory of finite groups : Theorem (Clifford) If $H$ is any normal subgroup of $G$ and $V$ is a semi-simple $k[G]$-module, then $V_{|H}$ is a semi-simple $k[H]$-module. | |
| Jun 5, 2011 at 6:46 | history | asked | sife | CC BY-SA 3.0 |