Cells of the weighted Coxeter group Cn
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摘要: 仿射 Weyl 群 (widetilde{C}_n,S) 可以看做仿射 Weyl群 (widetilde{A}_{2n},widetilde{S}) 在其某个满足alpha(widetilde{S})=widetilde{S} 的群自同构 alpha 下的固定点集合. widetilde{A}_{2n} 上的长度函数 widetilde{l}在 widetilde{C}_n 上的限制可以看做 widetilde{C}_n上的某个权函数. 本文通过研究仿射 Weyl 群 widetilde{A}_{2n} 在alpha 下的固定点集合从而 给出带有权函数的 Coxeter 群(widetilde{C}_n,widetilde{l}) 中对应于划分 bf{2^{n-1}1^3}的所有胞腔的清晰刻画.
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关键词:
- 仿射,Weyl,群 /
- 带有权函数的,Coxeter,群 /
- quad 拟分裂情形 /
- quad正整数,n,的划分 /
- quad 左胞腔 /
- quad 双边胞腔
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}. -
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