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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
9
votes
2
answers
883
views
Anisotropic algebraic groups have no unipotent elements
I have found the following fact stated in a number of places:
If $k$ is any field, a connected reductive group $G$ is anisotropic if and only if its only unipotent element is $e$ and $\mathrm{Hom}_k …
6
votes
2
answers
305
views
Real orbits of Complex Flag Varieties
Let $G$ be a semi-simple algebraic group over $\mathbb{C}$ with Borel subgroup $B$ and consider the flag variety $G/B$. If $G_0 \subset G$ is some real form, then $G_0$ acts on $G/B$ and decomposes t …