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The Weyl group of a root system is a subgroup generated by reflections through the hyperplanes orthogonal to the roots.

1 vote
0 answers
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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, …
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1 vote
0 answers
62 views

Minimal subrepresentation of the Weyl group

Background I want to generalize Theorem 3.2.1 in Dat, J., Orlik, S., & Rapoport, M. (2010). Period Domains over Finite and p-adic Fields (Cambridge Tracts in Mathematics). Cambridge: Cambridge Univers …
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  • 153
4 votes
1 answer
139 views

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, …
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