Timeline for Connected algebraic subgroup of $PGL_3$ and $PGL_2 \times PGL_2$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2017 at 10:07 | vote | accept | sabrebooth | ||
| Jul 19, 2017 at 8:18 | comment | added | sabrebooth | In the case of $PGL_3$ you also have a maximal conjugacy class for $PGL_2$, and again to be sure that you have only one conjugacy class for $SL_2$ (contained in a parabolic conjugacy class, so it doesn't yield maximal connected algebraic subrgoups of $PGL_3$) and one conjugacy class for $PGL_2$ (which yields maximal connected algebraic subrgoups of $PGL_3$), it seems that one needs Lie algebra arguments or at least some classifications results (like the paper of Seitz pointed out by Jim). | |
| Jul 19, 2017 at 6:23 | comment | added | Uri Bader | First you have max. parabolics. Putting this aside you can assume your groups is reductive. Moreover, it has no center, otherwise it is contained in a parablic. So it is semi-simple of rank 1 or 2. In both cases the rank 2 case must be the full group. The rank 1 case must be the irreducible rep of $\text{SL}_2$ in the case of $\text{PGL}_3$ and the graph of an automorphism in the product case. | |
| Jul 18, 2017 at 12:08 | answer | added | Anonymous | timeline score: 4 | |
| Jul 17, 2017 at 16:09 | answer | added | Jim Humphreys | timeline score: 8 | |
| Jul 17, 2017 at 15:26 | history | asked | sabrebooth | CC BY-SA 3.0 |