Left cells containing a fully commutative element

Let W be a finite or an affine Coxeter group and Wc the set of all the fully commutative elements in W. For any left cell L of W containing some fully commutative element, our main result of the paper is to prove that there exists a unique element (say wL) in L Wc such that any z L has the form z = xwL with (z) = (x) + (wL) for some x W. This implies that L is left connected, verifying a conjecture of Lusztig in our case.

• Type: Journal
• Year: 2006
• Where: JCT
• Authors: Jian-Yi Shi
• Keywords: Affine Coxeter Group, Commutative Element, JCT 2006, Unique Element