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Results tagged with reductive-groups
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user 4790
A reductive group is an algebraic group $G$ over an algebraically closed field such that the unipotent radical of $G$ is trivial
4
votes
Accepted
Can the intersection of a maximal parabolic with a closed sub-group contain more than one ma...
If $P$ is a parabolic subgroup of a reductive group $G$ and $H$ is a closed subgroup of $G$ containing $P$, then $G/H$ is a quotient of $G/P$, so it is projective, and $H$ is parabolic. It follows tha …
- 27k
13
votes
Accepted
commuting elements in a reductive group
Consider images in $\mathrm{PGL}_n$ of the matrices $A$ and $B$, where $A$ is the diagonal matrix whose $i^{\rm th}$ diagonal entry is $\omega^i$, where $\omega$ is a primitive $n^{\rm th}$ root of $ …
- 27k
7
votes
Accepted
Properness of reductive group actions on smooth varieties
Actions of reductive groups with finite stabilizers on quasi-projective varieties are often not proper. The simplest example I know is given by he action of $\mathrm{PGL}_2$ on the projective space $\ …
- 27k