# 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} }

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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