Let \alpha be a group automorphism of the affine Weyl group (\widetilde{A}_{2n},\widetilde{S}) with \alpha(\widetilde{S})=\widetilde{S}. Affine Weyl group(\widetilde{C}_n,S) can be seen as the fixed point set of the affine Weyl group (\widetilde{A}_{2n},\widetilde{S}) under its group automorphism \alpha. The restriction to \widetilde{C}_n of the length function \widetilde{l}_{2n} on \widetilde{A}_{2n} can be seen as a weight function on \widetilde{C}_n. In this paper, we
give the description for all the left and two-sided cells of the specific weighted Coxeter group (\widetilde{C}_3,\widetilde{l}_6) and prove that each left cell in (\widetilde{C}_3,\widetilde{l}_6) is left-connected.
YUE Ming-Shi
. Cells of the weighted Coxeter group (C3,l6)[J]. Journal of East China Normal University(Natural Science), 2016
, 2016(1)
: 27
-38
.
DOI: 10.3969/j.issn.1000-5641.2016.01.004
[1]LUSZTIG G. {Hecke algebra with unequal parameters]~[M]. Providence:American Mathmatical Society, 2003.
[2]SHI J Y. {The cells of the affine Weyl group \widetilde{C]_n in a certain quasi-split case]~[J]. J Algebra, 2015(422): 697-729.
[3]HUANG Q, SHI J Y. {Some cells in the weighted Coxeter group(\widetilde{C]_n,\widetilde{l]_{2n+1])]~[J]. J Algebra, 2013(395):63-81.
[4]岳明仕. {拟分裂情形下仿射~Weyl~群~\widetilde{C]_4~的胞腔]~[J].华东师范大学学报: 自然科学版, 2013(1): 61-75.
[5]SHI J Y. {The Kazhdan-Lusztig cells in certain affine Weyl groups]~[M]. Berlin: Springer-Verlag, 1986.
[6]GREENE C. {Some partitions associated with a partially ordered set]~[J]. J Comb Theory (A), 1976(20): 69-79.
[7]HUANG Q. \text{Left cells in the weighted Coxeter group\widetilde{C]_n]~[J]. J East China Norm Univ, 2013(1): 91-103.
[8]黄谦. {某些加权的~Coxeter~群的左胞腔]~[D]. 上海: 华东师范大学数学系,2013.
[9]YUE M S. \text{Cells of the affine Weyl group \widetilde{C]_n in quasi-split case]~[J]. J East China Norm Univ, 2014(3): 77-92.
[10]YUE M S. \text{Cells of the weighted Coxeter group\widetilde{C]_n]~[J]. J East China Norm Univ, 2015(3): 38-46.
[11]YUE M S. \text{Left cells of weighted Coxeter group(\widetilde{C]_n,\widetilde{l]_{2n])]~[J]. Advances in Mathematics(China), 2015, 44(4): 505-518.