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arXiv · 1903.00078

Conjectures P1-P15 for Coxeter groups with complete graph

Xun Xie
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Abstract

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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Xun Xie. 2019-02-28. Conjectures P1-P15 for Coxeter groups with complete graph. https://arxiv.org/abs/1903.00078

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