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Results tagged with root-systems
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user 65801
6
votes
Why, conceptually, does the torus normalizer in $G_2$ split?
While the following might not be conceptual, but at least it's simple if one knows group cohomology. The obstruction to splitting lives in $H^2(W;T)$, and we have $H^n(W;T)=0$ for all $n\geq 0$!
One w …
- 1,907
4
votes
Fixed Points of the Weyl Group action on a Maximal Torus and the Center of a Reductive Group
In general one has $T^W = Z(G) \times (\mathbb{Z}/2)^r$ where $r$ is the number of direct factors in $G$ isomorphic to $\text{SO}_{2n+1}$ ($n\geq 1$) except for the case $\text{char}(k)=2$ where $r=0$ …
- 1,907