应用数学与基础数学

带有权函数的Coxeter群Cn的胞腔

  • 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. E-mail: yuemingshi@lyu.edu.cn

收稿日期: 2014-08-07

  网络出版日期: 2015-05-28

基金资助

国家自然科学基金(11071073)

Cells of the weighted Coxeter group Cn

  • YUE Ming-Shi
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Received date: 2014-08-07

  Online 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.

本文引用格式

岳明仕 . 带有权函数的Coxeter群Cn的胞腔[J]. 华东师范大学学报(自然科学版), 2015 , 2015(3) : 38 -46 . DOI: 10.3969/j.issn.1000-5641.2015.03.006

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}.

参考文献

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