华东师范大学学报（自然科学版） >

2023 , Vol. 2023 >Issue 6: 1 - 13

DOI: https://doi.org/10.3969/j.issn.1000-5641.2023.06.001

数学

关于加权Coxeter群的胞腔理论的综述

  • 时俭益 ,
  • 黄谦
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  • 1. 华东师范大学 数学科学学院, 上海　200241
    2. 山西大学 数学科学学院, 太原　030006
时俭益, 男, 教授, 研究方向为Kazhdan-Lusztig 理论. E-mail: jyshi@math.ecnu.edu.cn

收稿日期: 2023-06-01

  网络出版日期: 2023-11-23

基金资助

国家自然科学基金(11471115); 上海市核心数学与实践重点实验室基金; 上海市科委项目(18dz2271000)

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A survey on the cell theory of weighted Coxeter groups

  • Jianyi SHI ,
  • Qian HUANG
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  • 1. School of Mathematical Sciences, East China Normal University, Shanghai　200241, China
    2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

Received date: 2023-06-01

  Online published: 2023-11-23

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摘要

介绍了在加权Coxeter群的胞腔理论方面所取得的成果, 详细描述了拟分裂情形下仿射Weyl群 $ \widetilde{C}_n $ 的胞腔分解, 简要描述了拟分裂情形下仿射Weyl群 $ \widetilde{B}_n $ 和一般情形下加权泛Coxeter群的胞腔分解1.

关键词： 仿射Weyl群; 加权Coxeter群; 拟分裂情形; 胞腔; 划分; 表

本文引用格式

时俭益 , 黄谦 . 关于加权Coxeter群的胞腔理论的综述[J]. 华东师范大学学报（自然科学版）, 2023 , 2023(6) : 1 -13 . DOI: 10.3969/j.issn.1000-5641.2023.06.001

Abstract

We give a survey on the contribution of our research group to the cell theory of weighted Coxeter groups. We present some detailed account for the description of cells of the affine Weyl group $ \widetilde{C}_n $ in the quasi-split case and a brief account for that of the affine Weyl group $ \widetilde{B}_n $ in the quasi-split case and of the weighted universal Coxeter group in general case.

Key words： affine Weyl group; weighted Coxeter group; quasi-split case; cells; partitions; tabloids

参考文献

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