华东师范大学学报(自然科学版) ›› 2016, Vol. 2016 ›› Issue (1): 27-38.doi: 10.3969/j.issn.1000-5641.2016.01.004

• 应用数学与基础数学 • 上一篇    下一篇

加权~Coxeter~群(C3,l6)的胞腔(英)

岳明仕   

  1. 临沂大学物流学院, 山东~~临沂  276000)
  • 收稿日期:2014-12-08 出版日期:2016-01-25 发布日期:2016-03-10
  • 通讯作者: 岳明仕, 男，讲师, 研究方向为~Heck~代数及表示理论. E-mail:lymsyue@gmail.com.
  • 作者简介:岳明仕, 男，讲师, 研究方向为~Heck~代数及表示理论.
  • 基金资助:

    国家自然科学基金(11071073)

Cells of the weighted Coxeter group (C3,l6)

YUE  Ming-Shi   

  • Received:2014-12-08 Online:2016-01-25 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

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

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