# Conjectures P1-P15 for Coxeter groups with complete graph

@article{Xie2019ConjecturesPF,
title={Conjectures P1-P15 for Coxeter groups with complete graph},
author={Xun Xie},
journal={arXiv: Representation Theory},
year={2019}
}
• Xun Xie
• Published 2019
• Mathematics
• arXiv: Representation Theory
We prove Lusztig's conjectures P1-P15 for Coxeter groups with complete graph, using deceasing induction on $\mathbf{a}$-values and a kind of decomposition formula of Kazhdan-Lusztig basis elements. As a byproduct, we give a description of the left, right, and two-sided cells. In the appendix, we prove P1-P15 for right-angled Coxeter groups by the same methods.
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