Jianwei Gao, Xun Xie
Abstract
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We prove Lusztig's conjectures P1-P15 for hyperbolic Coxeter groups of rank 3. Our proof enables us to give a description of the a-function and Kazhdan-Lusztig cells for these Coxeter groups.
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We prove Lusztig's conjectures P1-P15 for hyperbolic Coxeter groups of rank 3. Our proof enables us to give a description of the a-function and Kazhdan-Lusztig cells for these Coxeter groups.
Key concepts: Coxeter group, Rank (graph theory), Point group, Artin group, Mathematics, Coxeter complex, Combinatorics, Longest element of a Coxeter group