Fully commutative elements and Kazhdan-Lusztig cells in the finite and affine Coxeter groups, II

摘要

Let W be an irreducible finite or affine Coxeter group and let W-c be the set of fully commutative elements in W. We prove that the set W-c is closed under the Kazhdan-Lusztig preorder >=(LR) if and only if W-c is a union of two-sided cells of W.