Cells of the affine Weyl group $\widetilde{\bm C}_{\bm 4}$ in quasi-split case
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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.
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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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[1] {1}SHI\,J\,Y. The cells of affine Weyl groups $\widetilde{C}_n$ in acertain quasi-split case[EB/OL]. Preprint. [2012-12-29].http://math.ecnu.edu.cn/$^\thicksim$jyshi/myart/quasisplitl.pdf{2}LUSZTIG G. Hecke Algebras with Unequal Parameters [M]. CRM MonographSeries 18. Providence: {A}MS, 2003.{3}SHI J Y. The Kazhdan-Lusztig cells in certainaffine Weyl groups [M].Lecture Notes in Math 1179. Berlin: Springer-Verlag, 1986.{4}Greene C. Some partitions associated with a partially ordered set[J]. J Comb Theory(A), 1976, 20: 69-79. -
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