| The affine Coxeter group (Bn, S) can be realized as the fixed point set of the affine Coxeter group (Dm,S), m∈{2n,2n+1}, under a certain group automorphism αm，n with αm,n(S)=S. Let e be the length function of Dm. We give an explicit description for all the left cells L of (Bn, e) with a(L)≤6and show that each of these left cells is left-connected.Similarly, the affine Coxeter group (B3,S) can be realized as the fixed point set of the affine Coxeter group (D4, S) under a certain group automorphism a with a(S)=S. Let e be the length function of D4. We give an explicit description for all the left cells of the weighted Coxeter group (B3,e), then we show that each left (respectively, two-sided) cell of B3is left-(respectively, two-sided-)connected. |
