Cells of the weighted Coxeter group (B3, ?)
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摘要: 仿射Coxeter群(B3,S)可以被看做仿射Coxeter群(D4,S)在满足条件( S) = S的某种群自同构下的不动点集合,设l是D4的长度函数。本文明显地刻画了加权Coxeter群(B3,l)的所有左胞腔,同时证明了:加权Coxeter群(D4,L)和(B3,L)的所有左胞腔都是左连通的,所有双边胞腔都是双边连通的。
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关键词:
- 加权Coxeter群 /
- 拟分裂情形 /
- 胞腔 /
- 左连通性
Abstract: The affine Coxeter group ( e B3, S) can be realized as the fixed point set of the affine Coxeter group ( e D4, eS) under a certain group automorphism with ( eS) = eS. Let e? be the length function of e D4. We gave an explicit description for all the left cells of the weighted Coxeter group ( e B3, e?). Alsowe showed that in the the weighted Coxeter groups ( e D4, e?) and ( e B3, e?), each left (respectively, two-sided) cell was left-connected (respectively, two-sided-connected).-
Key words:
- weighted Coxeter group /
- quasi-split case /
- cells /
- left-connectedness
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