华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 1: 27 - 38

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.01.004

应用数学与基础数学

加权~Coxeter~群(C3,l6)的胞腔(英)

  • 岳明仕
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  • 临沂大学物流学院, 山东~~临沂  276000)
岳明仕, 男，讲师, 研究方向为~Heck~代数及表示理论.

收稿日期: 2014-12-08

  网络出版日期: 2016-03-10

基金资助

国家自然科学基金(11071073)

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Cells of the weighted Coxeter group (C3,l6)

  • YUE Ming-Shi
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Received date: 2014-12-08

  Online published: 2016-03-10

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摘要

{取~\alpha 是仿射~Weyl群~(\widetilde{A}_{2n},\widetilde{S}) 上某个满足~\alpha(\widetilde{S})=\widetilde{S} 的群自同构.仿射~Weyl 群~(\widetilde{C}_n,S) 可以看做仿射~Weyl 群\ (\widetilde{A}_{2n},\widetilde{S}) 在其群自同构~\alpha 下的固定点集合. \widetilde{A}_{2n} 上的长度函数\ \widetilde{l}_{2n} 在~\widetilde{C}_n 上的限制可以看做widetilde{C}_n 上的某个权函数. 本文给出了加权的~Coxeter 群\(\widetilde{C}_3,\widetilde{l}_6) 中所有左胞腔以及双边胞腔的清晰刻画并且证明 (\widetilde{C}_3,\widetilde{l}_6) 中的每个左胞腔都是左连通的.

关键词： 仿射~Weyl~群; 加权~Coxeter~群; 拟分裂情形; 整数~n~的划分;左胞腔

本文引用格式

岳明仕 . 加权~Coxeter~群(C3,l6)的胞腔(英)[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(1) : 27 -38 . DOI: 10.3969/j.issn.1000-5641.2016.01.004

Abstract

Let \alpha be a group automorphism of the affine Weyl group (\widetilde{A}_{2n},\widetilde{S}) with \alpha(\widetilde{S})=\widetilde{S}. Affine Weyl group(\widetilde{C}_n,S) can be seen as the fixed point set of the affine Weyl group (\widetilde{A}_{2n},\widetilde{S}) under its group automorphism \alpha. The restriction to \widetilde{C}_n of the length function \widetilde{l}_{2n} on \widetilde{A}_{2n} can be seen as a weight function on \widetilde{C}_n. In this paper, we
give the description for all the left and two-sided cells of the specific weighted Coxeter group (\widetilde{C}_3,\widetilde{l}_6) and prove that each left cell in (\widetilde{C}_3,\widetilde{l}_6) is left-connected.

Key words： affine Weyl group; weighted Coxeter group; quasi-split case; partitions of n; left cells

参考文献

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