Timeline for Reference request: representations of unipotent groups have a fixed point.
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2011 at 3:36 | comment | added | Keerthi Madapusi | Here's an argument that might finish things in general using Borel's result: if a unipotent group is not connected (which can only happen in characteristic $p$), then its group of connected components $\pi_0$ has $p$-power order and the sub-space of fixed points of the connected component containing the identity is stable under $\pi_0$. So it suffices to show that every representation of a finite $p$-group on a characteristic $p$ vector space has a fixed point. One can now reduce to the case of a finite field, and use the orbit-stabilizer theorem. | |
| Feb 3, 2011 at 3:22 | vote | accept | Keerthi Madapusi | ||
| Feb 3, 2011 at 3:22 | comment | added | Keerthi Madapusi | Ah, thank you! Also, I guess I was only imagining unipotent groups as successive extensions of $\mathbb{G}_a$, but it's nice to know that the result is valid in general. | |
| Feb 3, 2011 at 3:16 | vote | accept | Keerthi Madapusi | ||
| Feb 3, 2011 at 3:16 | |||||
| Feb 3, 2011 at 3:08 | history | answered | Evan Jenkins | CC BY-SA 2.5 |