Left cells containing a fully commutative element

Authors:
Jian-Yi Shi
Affiliations:
Department of Mathematics, East China Normal University, Shanghai, PR China and Center for Combinatorics, Nankai University, Tianjin, PR China
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

Citing 3
Cited 0

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Abstract

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 l(z) = l(x) + l(wL) for some x ∈ W. This implies that L is left connected, verifying a conjecture of Lusztig in our case.