W-graph ideals II

In Howlett and Nguyen (2010) [5], , the concept of a W-graph ideal in a Coxeter group was introduced, and it was shown how a W-graph can be constructed from a given W-graph ideal. In this paper, we describe a class of W-graph ideals from which certain Kazhdan–Lusztig left cells arise. The result justifies the algorithm as illustrated in Howlett and Nguyen (2010) [5] for the construction of W-graphs for Specht modules for the Hecke algebra of type A.