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Results tagged with reductive-groups
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user 504919
A reductive group is an algebraic group $G$ over an algebraically closed field such that the unipotent radical of $G$ is trivial
5
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An example of a Deligne–Lusztig variety for a general linear group
Take $G=\operatorname{GL}_3$, defined over the algebraic closure of a finite field $\mathbb{F}_q$ and let $X$ be the set of Borel subgroups of $G$.
The Frobenius morphism $F:G\to G$ induces a map $F: …
- 153
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0
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Relative position of flags for the general linear group
This question is related my question in An example of a Deligne–Lusztig variety for a general linear group, and the obtained answer.
Situation
I am working with the general linear group. Specifically, …
- 153
2
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0
answers
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Relative position of Borel subgroups for the symplectic group
Background
Let $n$ be a positive integer, let $W$ be the Weyl group of $\text{GL}_n$.
Its set of Borel subgroups is isomorphic to the full flag variety $\mathcal{F}_n$.
In this question, I studied wha …
- 153
4
votes
1
answer
139
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Cohomology of Deligne-Lusztig variety associated to Coxeter element
Determining the individual ($l$-adic) cohomology groups of Deligne-Lusztig varieties has only been done for the general linear group and for some other very specific cases (as far as I know).
However, …
- 153
2
votes
1
answer
128
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Relative position of flags and the Robinson-Schensted correspondence
This question is related my question in An example of a Deligne–Lusztig variety for a general linear group, and the obtained answer.
I am currently reading Steinberg, Robert, An occurrence of the Robi …
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