华东师范大学学报(自然科学版)

• 数学 •    下一篇

某种拟分裂情形下加权Coxeter群(\widetilde C_n,\tilde l_{2n})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:2015-05-27 出版日期:2016-07-25 发布日期:2016-09-29
  • 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.
  • 基金资助:

    国家自然科学基金(11071073)

Cells of the weighted Coxeter group\\ (~\bmC\bmn,~\bml2\bmn) in a certain quasi-split case

YUE Ming-shi   

  1. School of Logistics, Linyi University, Linyi Shandong 276000, China
  • Received:2015-05-27 Online:2016-07-25 Published:2016-09-29

摘要:

仿射Weyl群(˜Cn,S)可以看作仿射Weyl群(˜A2n,˜S) 在其某个满足α(˜S)=˜S的群自同构α下的固定点集合. ˜A2n上的长度函数˜l2n˜Cn上的限制可以看做˜Cn上的权函数. 通过研究(˜A2n,˜S)α下的固定点集合,本文刻画了加权Coxeter群(˜Cn,˜l2n)对应于划分332n4的所有胞腔. 证明了文中左胞腔的左连通性,从而验证了Lusztig提出的一个猜想.

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

Abstract:

The fixed point set of the affine Weyl group (˜A2n,˜S) under its group automorphism α with α(˜S)=˜S can be seen as the affine Weyl group (˜Cn,S). The restriction to ˜Cn of the length function ˜l2n on ˜A2n can be seen as a weight function on ˜Cn. In the present paper, by studying the fixed point set of the affine Weyl group (˜A2n,˜S) under α, we give the description for all the cells of the weighted Coxeter group (˜Cn,˜l2n) corresponding to the specific partition 332n4. We also prove that each left cell we considered in this paper is left-connected, verifying a conjecture of Lusztig in our case.

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