On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials
Combinatorics
2025-06-04 v3 Representation Theory
Abstract
We show that the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic version that we introduce, are equivalent. We use this to give a new proof of Marietti's conjecture in the case of lower Bruhat intervals and to prove several new cases of the parabolic conjectures.
Keywords
Cite
@article{arxiv.2404.04246,
title = {On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials},
author = {Grant T. Barkley and Christian Gaetz},
journal= {arXiv preprint arXiv:2404.04246},
year = {2025}
}
Comments
v3: final version, to appear in Selecta Mathematica