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Hypercube Richardson varieties from magic words

  • Balázs Elek
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Abstract

Inspired by the recent preprint of Ellenberg, Libedinsky, Plaza, Simental, and Williamson, we study the geometry of Richardson varieties whose associated Bruhat intervals are boolean posets. We define magic words for a Bruhat interval and prove that for intervals with magic words the associated Richardson variety is a tower of ℙ1-s. We also prove that the Bruhat intervals consisting of the dyadically well-distributed permutations all have magic words. This gives a new proof that they form a boolean poset.

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Cite

BibTeXRIS
BibTeX
@misc{elek2026hypercube,
  title = {{Hypercube Richardson varieties from magic words}},
  author = {Balázs Elek},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22730},
  eprint = {2610.22730},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22730},
}
RIS
TY  - UNPB
TI  - Hypercube Richardson varieties from magic words
AU  - Balázs Elek
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22730
UR  - https://arxiv.org/abs/2610.22730
AB  - Inspired by the recent preprint of Ellenberg, Libedinsky, Plaza, Simental, and Williamson, we study the geometry of Richardson varieties whose associated Bruhat intervals are boolean posets. We define magic words for a Bruhat interval and prove that for intervals with magic words the associated Richardson variety is a tower of ℙ^1-s. We also prove that the Bruhat intervals consisting of the dyadically well-distributed permutations all have magic words. This gives a new proof that they form a boolean poset.
ER  -