Timeline for Outer automorphisms of Borel subgroup
Current License: CC BY-SA 3.0
3 events
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| Mar 6, 2013 at 0:55 | comment | added | Jim Humphreys |
@Dmitri: The case $p=2$ does have a different flavor (with the torus disappering). In general I don't know how to characterize $B$ as an abstract group in a way that helps with the automorphism problem.. Beyond the special linear group, it may turn out that thinking about Borel subgroups or related Lie theory isn't helpful at all. The original notion was tied strongly to the role of this subgroup within a well-behaved larger group, even over a finite field.
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| Mar 5, 2013 at 21:37 | comment | added | Dmitri Nikshych | Thanks! Sure $B$ coincides with its normalizer in $GL(n, F)$. But it appears that there are non-trivial outer automorphisms of $B$ , e.g., coming from automorphisms of $F$. Also, in this paper deepblue.lib.umich.edu/handle/2027.42/30473 the group $Out(B)$ is computed when $F$ is the field of $2$ elements. It is surprisingly large (in this case, of course, $B$ is the group of unipotent upper-triangular matrices) | |
| Mar 5, 2013 at 21:16 | history | answered | Jim Humphreys | CC BY-SA 3.0 |