加权Coxeter群(_3,)的胞腔(英文)

Cells of the weighted Coxeter group (_3,)

仿射Coxeter群(_3,S)可以被看做仿射Coxeter群(D_4,S)在满足条件α(S)=S的某种群自同构α下的不动点集合,设是D_4的长度函数.本文明显地刻画了加权Coxeter群(_3,)的所有左胞腔.同时证明了:加权Coxeter群(D_4,)和(_3,)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.

The affine Coxeter group （-B3,S） can be realized as the fixed point set of the affine Coxeter group （-D4,-S） under a certain group automorphism α with α（-S） =-S.Let -l be the length function of -D4.We gave an explicit description for all the left cells of the weighted Coxeter group （-B3,-L）.Also,we showed that in the the weighted Coxeter groups （-D4,-l） and （-B3,-l）,each left （respectively,two-sided） cell was left-connected （respectively,two-sided-connected）.