Relative Rouquier linearity and inverse hybrid Kazhdan-Lusztig positivity

Kaixuan Gan; Xun Xie; Qifan Zhou

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arXiv · 2611.00882

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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BibTeX RIS

Kaixuan Gan, Xun Xie, Qifan Zhou. 2026-10-31. Relative Rouquier linearity and inverse hybrid Kazhdan-Lusztig positivity. https://arxiv.org/abs/2611.00882

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