The cells of the affine Weyl group C˜n in a certain quasi-split case, II

The affine Weyl group (C˜n,S) can be realized as the fixed point set of the affine Weyl group (A˜2n−1,S˜) under a certain group automorphism α with α(S˜)=S˜. Let ℓ˜ be the length function of A˜2n−1. The main results of the paper are to prove the left-connectedness of any left cell of the weighted Coxeter group (C˜n,ℓ˜) in the set Eλ for any nice λ∈Λ2n, to prove all the partitions (2n−k,k) with 1≤k≤n being nice and to describe all the cells of (C˜n,ℓ˜) in the set E(2n−k,k).