华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (1): 61-75.

• 应用数学与基础数学 • 上一篇    下一篇

拟分裂情形下仿射\,Weyl 群\,$\widetilde{\bm C}_{\bm 4}$~的胞腔

岳明仕   

  1. 华东师范大学~~数学系, 上海 200241
  • 收稿日期:2012-02-01 修回日期:2012-05-01 出版日期:2013-01-25 发布日期:2013-01-18

Cells of the affine Weyl group $\widetilde{\bm C}_{\bm 4}$ in quasi-split case

YUE Ming-shi   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2012-02-01 Revised:2012-05-01 Online:2013-01-25 Published:2013-01-18

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摘要： 仿射~Weyl~群\,$(\widetilde{C}_4,\,S)$\,可被看成仿射\,Weyl\,群\,$(\widetilde{A}_7,\,\widetilde{S})$~在某个群自同构\,$\alpha$\,下的不动点集合.
记\,$\widetilde{l}:\widetilde{A}_7\longrightarrow
\mathbf{\mathbf{N}}$\,是仿射\,Weyl\,群\,$\widetilde{A}_7$\,上的长度函数.
则\,$\widetilde{l}$\,在\,$\widetilde{C}_4$\,上的限制为\,$\widetilde{C}_4$\,的权函数记作\,$L$.
本文给出带权\,Coxeter\,群\,$(\widetilde{C}_4,\,L)$\,的胞腔分解.

关键词: 仿射~Weyl~群, 带权的\,Coxeter\,群, 拟分裂情形, 胞腔, 划分

Abstract: The affine Weyl group $(\widetilde{C}_4,\,S)$ can be
considered as the fixed point set of the affine Weyl group
$(\widetilde{A}_7,\,\widetilde{S})$ under a certain group
automorphism $\alpha$. Let
$\widetilde{l}:\widetilde{A}_7\longrightarrow \mathbf{\mathbf{N}}$
be the length function of\,$\widetilde{A}_7$. The restriction of
$\widetilde{l}$ on $\widetilde{C}_4$, denoted by $L$, is a weighted
function on $\widetilde{C}_4$. This paper classified the cells in
weighted Coxteger group\,$(\widetilde{C}_4,\,L)$.

Key words: \!\!affine Weyl group, \!weighted Coxeter group, \!quasi-split case, \!cell, \!\!partition

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