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Unipotent quotients in compactified Coxeter varieties

  • Joseph Muller
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Abstract

In this paper, we extend Lusztig's description of quotients of Coxeter varieties by unipotent radicals of parabolic subgroups, to quotients of certain open neighbourhoods in the smooth compactification of Coxeter varieties. These quotients are products of an affine space with a Coxeter variety for an associated Levi quotient, and this result holds uniformly for any connected reductive group over a finite field. As an application, we prove a conjecture of Wang computing the invariants, under the action of unipotent subgroups, of the cohomology of the Deligne-Lusztig coverings of Coxeter varieties. We also prove that derived Alvis-Curtis duality sends the compactly supported cohomology of these coverings to their ordinary cohomology.

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Cite

BibTeXRIS
BibTeX
@misc{muller2026unipotent,
  title = {{Unipotent quotients in compactified Coxeter varieties}},
  author = {Joseph Muller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15278},
  eprint = {2610.15278},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15278},
}
RIS
TY  - UNPB
TI  - Unipotent quotients in compactified Coxeter varieties
AU  - Joseph Muller
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15278
UR  - https://arxiv.org/abs/2610.15278
AB  - In this paper, we extend Lusztig's description of quotients of Coxeter varieties by unipotent radicals of parabolic subgroups, to quotients of certain open neighbourhoods in the smooth compactification of Coxeter varieties. These quotients are products of an affine space with a Coxeter variety for an associated Levi quotient, and this result holds uniformly for any connected reductive group over a finite field. As an application, we prove a conjecture of Wang computing the invariants, under the action of unipotent subgroups, of the cohomology of the Deligne-Lusztig coverings of Coxeter varieties. We also prove that derived Alvis-Curtis duality sends the compactly supported cohomology of these coverings to their ordinary cohomology.
ER  -