Abstract: Affine Weyl group (widetilde{C}_n,S) can be seen as a fixed point set of the affine Weyl group (widetilde{A}_{2n},widetilde{S}) under a certain group
automorphism alpha of widetilde{A}_{2n} with alpha(widetilde{S})=widetilde{S}. Let widetilde{l} be the length function on widetilde{A}_{2n}. The restriction to
widetilde{C}_n of widetilde{l} on widetilde{A}_{2n} can be seen as a weight function on widetilde{C}_n. In this paper, by studying the fixed point set of the affine Weyl group widetilde{A}_{2n} under alpha, we can give the description of all the cells of weighted Coxeter group (widetilde{C}_n,widetilde{l}) corresponding to the partition bf{2^{n-1}1^3}.

Key words: affine Weyl group, quad weighted Coxetergroup, quad quasi-split case, quad partitions of the positive integer n, quad left cells, quad two-sided cells