加权Coxeter群(B3, l)的胞腔

doi:10.3969/j.issn.1000-5641.2015.01.004

华东师范大学学报(自然科学版) ›› 2015, Vol. 2015 ›› Issue (1): 27-41.doi: 10.3969/j.issn.1000-5641.2015.01.004

加权Coxeter群(B₃, l)的胞腔

米倩倩^1,时俭益²

1. 无锡职业技术学院基础课部, 江苏无锡 214121 2.华东师范大学数学系上海 200241

收稿日期:2013-12-01 出版日期:2015-01-25 发布日期:2015-03-29
通讯作者: 米倩倩,女, 讲师. 研究方向为代数群. E-mail:minaiqnaiq@163.com
作者简介:第二作者:时俭益, 男, 教授. 研究方向为代数群、代数组合论.E-mail: jyshi@math.ecnu.edu.cn.
基金资助:
国家自然科学基金(11071073, 11131001);

教育部高校博士点基金(1439864);

上海市科委基金(11XD1402200)

Cells of the weighted Coxeter group (B₃, ?)

MI Qian-Qian¹, SHI Jian-Yi²

Received:2013-12-01 Online:2015-01-25 Published:2015-03-29

摘要/Abstract

摘要： 仿射Coxeter群(B₃,S)可以被看做仿射Coxeter群(D₄,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。

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 α with α( 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?). Also§we 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

中图分类号:

米倩倩, 时俭益. 加权Coxeter群(B₃, l)的胞腔[J]. 华东师范大学学报(自然科学版), 2015, 2015(1): 27-41.

MI Qian-Qian, SHI Jian-Yi. Cells of the weighted Coxeter group (B₃, ?)[J]. Journal of East China Normal University(Natural Sc, 2015, 2015(1): 27-41.

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加权Coxeter群(B₃, l)的胞腔

Cells of the weighted Coxeter group (B₃, ?)

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