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Results tagged with reductive-groups
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user 22846
A reductive group is an algebraic group $G$ over an algebraically closed field such that the unipotent radical of $G$ is trivial
3
votes
The centralizer of a semisimple element which is not contained in any proper parabolic subgr...
What you want is a specific part of something that fits into a wider framework due to Borel--Tits. Specifically, you're looking for Theorem 4.15 and Corollary 4.16 of "Groupes réductifs", Inst. Hautes …
- 2,902
3
votes
Accepted
Regular embeddings of reductive groups
I had cause to think about this exercise recently so I thought I’d write an answer. I think Jim’s answer is sufficient but as you seem to want more details I’ll provide them here. I am aware that you …
- 2,902
7
votes
Accepted
Unipotent orbit in adjoint group over finite field
That's not what they're claiming and your statement is not true. Your claim is that every unipotent element is rational. However Lemma 5.6 of this article by Tiep and Zalesskii provides a counter exam …
- 2,902
6
votes
Accepted
Principal series of finite group of Lie type
So, I think the answer to your question is yes. This may not be the slickest proof but I think it works. Firstly let $\mathrm{pr}_G$ be the projection map from the space of all class functions to the …
- 2,902