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PreprintarXiv licencearXiv

Relative Rouquier linearity and inverse hybrid Kazhdan-Lusztig positivity

  • Kaixuan Gan
  • Xun Xie
  • Qifan Zhou
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Abstract

We prove signed positivity for the expansion of a parabolic hybrid basis in the Kazhdan-Lusztig basis of a Hecke algebra. The coefficients have degree bounded by the length of the corresponding minimal coset representative. We deduce this linearity from Elias-Williamson's ordinary Rouquier linearity by a truncation argument. The result does not require the parabolic subgroup to be finite.

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Cite

BibTeXRIS
BibTeX
@misc{gan2026relative,
  title = {{Relative Rouquier linearity and inverse hybrid Kazhdan-Lusztig positivity}},
  author = {Kaixuan Gan and Xun Xie and Qifan Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00882},
  eprint = {2611.00882},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00882},
}
RIS
TY  - UNPB
TI  - Relative Rouquier linearity and inverse hybrid Kazhdan-Lusztig positivity
AU  - Kaixuan Gan
AU  - Xun Xie
AU  - Qifan Zhou
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00882
UR  - https://arxiv.org/abs/2611.00882
AB  - We prove signed positivity for the expansion of a parabolic hybrid basis in the Kazhdan-Lusztig basis of a Hecke algebra. The coefficients have degree bounded by the length of the corresponding minimal coset representative. We deduce this linearity from Elias-Williamson's ordinary Rouquier linearity by a truncation argument. The result does not require the parabolic subgroup to be finite.
ER  -