Bounded Bruhat intervals and affine Coxeter groups

@misc{barkley2026bounded,
  title = {{Bounded Bruhat intervals and affine Coxeter groups}},
  author = {Grant T. Barkley and Christian Gaetz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.16894},
  eprint = {2606.16894},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.16894},
}

TY  - UNPB
TI  - Bounded Bruhat intervals and affine Coxeter groups
AU  - Grant T. Barkley
AU  - Christian Gaetz
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2606.16894
UR  - https://arxiv.org/abs/2606.16894
AB  - Dyer (1991) proved that, for each fixed length k, only finitely many isomorphism types of Bruhat intervals occur in finite Coxeter groups. In this short paper, we prove that this result holds also for affine Coxeter groups, and moreover that this characterizes the affine groups among all infinite Coxeter groups. We also show that the coefficients of q in the Kazhdan-Lusztig polynomials of a Coxeter group are bounded if and only if the group is finite or affine.
ER  -