Cells of the weighted Coxeter group (C3,l6)
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摘要: {取~\alpha 是仿射~Weyl群~(\widetilde{A}_{2n},\widetilde{S}) 上某个满足~\alpha(\widetilde{S})=\widetilde{S} 的群自同构.仿射~Weyl 群~(\widetilde{C}_n,S) 可以看做仿射~Weyl 群\ (\widetilde{A}_{2n},\widetilde{S}) 在其群自同构~\alpha 下的固定点集合. \widetilde{A}_{2n} 上的长度函数\ \widetilde{l}_{2n} 在~\widetilde{C}_n 上的限制可以看做widetilde{C}_n 上的某个权函数. 本文给出了加权的~Coxeter 群\(\widetilde{C}_3,\widetilde{l}_6) 中所有左胞腔以及双边胞腔的清晰刻画并且证明 (\widetilde{C}_3,\widetilde{l}_6) 中的每个左胞腔都是左连通的.
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关键词:
- 仿射~Weyl~群 /
- 加权~Coxeter~群 /
- 拟分裂情形 /
- 整数~n~的划分 /
- 左胞腔
Abstract: 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. -
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