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. 
2 Citations