Timeline for Restrictions of Modules and Dimensions
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21, 2012 at 12:26 | vote | accept | dward1996 | ||
| Feb 20, 2012 at 14:02 | answer | added | daveh | timeline score: 1 | |
| Feb 20, 2012 at 12:24 | history | edited | dward1996 | CC BY-SA 3.0 |
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| Feb 20, 2012 at 11:07 | comment | added | dward1996 | Having looked at this again, I'm not sure that I follow the comment by mt. My initial reasoning was as follows. Suppose M were a 5-dimensional module. If M has a 4-dimensional submodule, then it must have a 1-dimensional quotient over K, which we know is not the case. Thus it must be the case that every irreducible submodule of M is 1-dimensional over K. However, the restriction of M to KR has a 2-dimensional irreducible submodule. A similar argument shows that M must have a 4-dimensional irreducible submodule, and thus as M has dimension at most 4, it is an irreducible 4-dimensional module | |
| Feb 14, 2012 at 15:24 | comment | added | dward1996 | I think your answer has also proved that irrespective of the answer to the question in my specific case, there is a flaw in my reasoning. Thanks for the help. | |
| Feb 14, 2012 at 15:10 | comment | added | dward1996 | Sorry, P and R are parabolic subgroups of the McLaughlin Group in a minimal parabolic system. | |
| Feb 14, 2012 at 14:02 | comment | added | M T | The answer is no if and only if $\operatorname{Ext}^1(4,1)\neq 0$ in the obvious notation. If you said what P and R are maybe someone could work it out, but a priori it is not even obvious groups with these properties exist. | |
| Feb 14, 2012 at 13:42 | history | asked | dward1996 | CC BY-SA 3.0 |