华东师范大学学报（自然科学版） >

2015 , Vol. 2015 >Issue 1: 27 - 41

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.01.004

应用数学与基础数学

加权Coxeter群(B3, l)的胞腔

  • 米倩倩 ,
  • 时俭益
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  • 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
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.

收稿日期: 2013-12-01

  网络出版日期: 2015-03-29

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)

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Cells of the weighted Coxeter group (B3, ?)

  • MI Qian-Qian ,
  • SHI Jian-Yi
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Received date: 2013-12-01

  Online published: 2015-03-29

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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

本文引用格式

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 . DOI: 10.3969/j.issn.1000-5641.2015.01.004

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

参考文献

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