Cells of the affine Weyl group $\widetilde{\bm C}_{\bm n}$ in quasi-split case
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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.
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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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[1] {1} LUSZTIG G. {Hecke algebra with unequal parameters}~[M].~CRM Monograph Series 18. AMS, 2003.{2} SHI J Y. {Cells of the affine Weyl group $\widetilde{C}_n$ in a quasi-split case} [EB/OL]. [2012-12-29]. http://math.ecnu.edu.cn/\\$^\sim$jyshi/myart/quasisplit1.pdf.{3} SHI J Y. {The Kazhdan-Lusztig cells in certain affine Weyl groups}~[M]. Lecture Notes in Math 1179. Springer-Verlag, 1986.{4} GREENE C. {Some partitions associated with a partially ordered set}~[J]. J Comb Theory(A), 1976,20(1): 69-79{5} HUANG Q. {Left cells in the weighted Coxeter group $\widetilde{C}_n$}~[J]. Journal of East China Normal University (Natural scinece), 2013(1): 91-103.{6} SHI J Y. {The partial order on two-sided cells of certain affine Weyl groups}~[J]. J Algebra, 1996, 179(2): 607-621.{7} YUE M S. {The left cells of affine Weyl group $\widetilde{C}_4$ in quasi-split case}~[J]. Journal of East China Normal University (Natural scinece), 2013(1): 61-75. -
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