华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (3): 77-92.

• 数学 • 上一篇    下一篇

拟分裂情形下仿射Weyl群$\widetilde{\bm C}_{\bm n}$的胞腔

岳明仕   

  1. 临沂大学~物流学院, 山东 临沂 276000
  • 收稿日期:2013-05-01 修回日期:2013-08-01 出版日期:2014-05-25 发布日期:2014-07-25

Cells of the affine Weyl group $\widetilde{\bm C}_{\bm n}$ in quasi-split case

YUE Ming-shi   

  1. Department of Logistics, Linyi University, Linyi Shandong 276000, China
  • Received:2013-05-01 Revised:2013-08-01 Online:2014-05-25 Published:2014-07-25

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摘要： 仿射\ Weyl 群\ $\widetilde{C}_n$ 可以看做仿射\ Weyl 群\
$\widetilde{A}_{2n}$ 在某个群自同构下的固定点集合. 通过研究\
$\widetilde{A}_{2n}$ 在这个群自同构下的固定点集合, 可以给出加权的\
Coxeter 群\ $\widetilde{C}_n$ 对应于划分\ $\bf{2^{n}1}$
的所有胞腔的清晰刻画.

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

Abstract: The affine Weyl group $\widetilde{C}_n$ under a certain
automorphism of $\widetilde{A}_{2n}$ can be seen as a fixed point
set of the affine Weyl group $\widetilde{A}_{2n}$. By giving an
explicit description of the fixed point set of $\widetilde{A}_{2n}$
under this automorphism, we shall give the explicit description of
the cells in weighted Coxeter group $\widetilde{C}_n$ corresponding
to the partition $\bf{2^{n}1}$.

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

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