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PreprintCC BY 4.0arXiv

Buildings governed by twisted Bruhat orders

  • Harvey Sykes
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Abstract

This paper introduces the notion of a twisted building associated to a Coxeter system and an initial section of a reflection order. These are pairs of buildings and a map between them which depends on a twisted Bruhat order. It is proved that projection maps exist between components and that the common apartment property holds for a suitable notion of an apartment, generalising what is known for twin buildings. Several well-known examples are given, including a family of twisted buildings associated to an affine building and its façades.

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Cite

BibTeXRIS
BibTeX
@misc{sykes2026buildings,
  title = {{Buildings governed by twisted Bruhat orders}},
  author = {Harvey Sykes},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02925},
  eprint = {2611.02925},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02925},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Buildings governed by twisted Bruhat orders
AU  - Harvey Sykes
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02925
UR  - https://arxiv.org/abs/2611.02925
AB  - This paper introduces the notion of a twisted building associated to a Coxeter system and an initial section of a reflection order. These are pairs of buildings and a map between them which depends on a twisted Bruhat order. It is proved that projection maps exist between components and that the common apartment property holds for a suitable notion of an apartment, generalising what is known for twin buildings. Several well-known examples are given, including a family of twisted buildings associated to an affine building and its façades.
ER  -