华东师范大学学报(自然科学版) ›› 2015, Vol. 2015 ›› Issue (3): 38-46.doi: 10.3969/j.issn.1000-5641.2015.03.006

• 应用数学与基础数学 • 上一篇    下一篇

带有权函数的Coxeter群Cn的胞腔

岳明仕   

  1. 临沂大学 物流学院, 山东 临沂 276000
  • 收稿日期:2014-08-07 出版日期:2015-05-25 发布日期:2015-05-28
  • 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:yuemingshi@lyu.edu.cn
  • 作者简介:岳明仕, 男, 讲师,研究方向为,Heck,代数及表示理论. E-mail: yuemingshi@lyu.edu.cn
  • 基金资助:

    国家自然科学基金(11071073)

Cells of the weighted Coxeter group Cn

YUE Ming-shi   

  • Received:2014-08-07 Online:2015-05-25 Published:2015-05-28

摘要: 仿射 Weyl 群 (widetilde{C}_n,S) 可以看做仿射 Weyl群 (widetilde{A}_{2n},widetilde{S}) 在其某个满足alpha(widetilde{S})=widetilde{S} 的群自同构 alpha
下的固定点集合. widetilde{A}_{2n} 上的长度函数 widetilde{l}在 widetilde{C}_n 上的限制可以看做 widetilde{C}_n上的某个权函数. 本文通过研究仿射 Weyl 群  widetilde{A}_{2n} 在alpha 下的固定点集合从而 给出带有权函数的 Coxeter 群(widetilde{C}_n,widetilde{l}) 中对应于划分 bf{2^{n-1}1^3}的所有胞腔的清晰刻画.

关键词: 仿射,Weyl,群, 带有权函数的,Coxeter,群, quad 拟分裂情形, quad正整数,n,的划分, quad 左胞腔, quad 双边胞腔

Abstract: Affine Weyl group (widetilde{C}_n,S) can be seen as a fixed point set of the affine Weyl group (widetilde{A}_{2n},widetilde{S}) under a certain group
automorphism alpha of widetilde{A}_{2n} with alpha(widetilde{S})=widetilde{S}. Let widetilde{l} be the length function on widetilde{A}_{2n}. The restriction to
widetilde{C}_n of widetilde{l} on widetilde{A}_{2n} can be seen as a weight function on widetilde{C}_n. In this paper, by studying the fixed point set of the affine Weyl group widetilde{A}_{2n} under alpha, we can give the description of all the cells of weighted Coxeter group (widetilde{C}_n,widetilde{l}) corresponding to the partition bf{2^{n-1}1^3}.

Key words: affine Weyl group, quad weighted Coxetergroup, quad quasi-split case, quad partitions of the positive integer n, quad left cells, quad two-sided cells

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