W-graphs for Hecke algebras with unequal parameters
In (Howlett and Nguyen in J Algebra 361:188–212, 2012), the concept of W-graph ideal in a Coxeter group was introduced, and it was showed that a W-graph can be constructed from a given W-graph ideal (this is the case of equal parameters). In this paper, we generalize the definition of W-graph ideal in the weighted Coxeter groups, and describe how to construct a W-graph from a given W-graph ideal in the case of unequal parameters.