Abstract

For extra-large Coxeter systems (m(s, r) > 3), we construct a natural and explicit set of Soergel bimodules D = {D(w)}(w is an element of W) such that each D. contains as a direct summand (or is equal to) the indecomposable Soergel bimodule B(w). When decategorified, we prove that D gives rise to a set {d(w)}(w is an element of W) that is actually a basis of the Hecke algebra. This basis is close to the Kazhdan-Lusztig basis and satisfies a positivity condition. (C) 2011 Elsevier Inc. All rights reserved.