加权的~Coxeter~群~$\widetilde{\bm C}_{\bm n}$~的左胞腔

黄谦

加权的~Coxeter~群~$\widetilde{\bm C}_{\bm n}$~的左胞腔

黄谦

1.
华东师范大学数学系, 上海 200241

详细信息

中图分类号: O15
计量
- 文章访问数: 2326
- HTML全文浏览量: 22
- PDF下载量: 1753
- 被引次数: 0
出版历程
- 收稿日期: 2012-02-01
- 修回日期: 2012-05-01
- 刊出日期: 2013-01-25

Left cells in the weighted Coxeter group ${\bm {\widetilde C}_{\bm n}}$

HUANG Qian

1.
Department of Mathematics, East China Normal University,Shanghai 200241, China

摘要

摘要: 仿射~Weyl~群~($\widetilde{A}_{2n},\widetilde{S}$) 在某个群同构~$\alpha$~(其中~$\alpha(\widetilde{S}) = \widetilde{S}$)~下的固定点集合能被看作是仿射~Weyl~群~($\widetilde{C}_n,S$). 那么加权的~Coxeter~群\ ($\widetilde{C}_n,\widetilde{\ell}$)的左和双边胞腔($\widetilde{\ell}$ 是仿射~Weyl~群~$\widetilde{A}_{2n}$~的长度函数), 就能通过研究仿射~Weyl~群~($\widetilde{A}_{2n},\widetilde{S}$) 在群同构~$\alpha$~下的固定点集合而给出一个清晰的划分. 因此给出了加权的~Coxeter~群~($\widetilde{C}_n,\widetilde{\ell}$) 对应于划分\ $\textbf{k}\textbf{1}^{\textbf{2n+1-k}}$~和~$(2n-1,2)$ 的所有左胞腔的清晰刻画, 这里对所有的~$1\leqslant k \leqslant 2n+1$.
- 仿射~Weyl~群 /
- 左胞腔 /
- 拟分裂 /
- 加权的~Coxeter~群
Abstract: The fixed point set of the affine Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under a certain group automorphism $\alpha$ with $\alpha\,(\widetilde{S}) = \widetilde{S}$ can be considered as the affine Weyl group ($\widetilde{C}_n,S$). Then the left and two-sided cells of the weighted Coxeter group ($\widetilde{C}_n,\widetilde{\ell}$), where $\widetilde{\ell}$ is the length function of $\widetilde{A}_{2n}$, can be given an explicit description by studying the fixed point set of the affine Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under $\alpha$. We describe the cells of ($\widetilde{C}_n,\widetilde{\ell}$) corresponding to the partitions $\textbf{k}\textbf{1}^{\textbf{2n+1-k}}$ with $1\leqslant k \leqslant 2n+1$ and $(2n-1,2)$.
- affine Weyl groups /
- left cells /
- quasi-split case /
- weighted Coxeter group

HTML全文

参考文献(1)

[1]

{1}

LUSZTIG G. Hecke algebras with unequal parameters [M]. Providence:

American Mathematical Society, 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/

$^\thicksim$jyshi/myart/quasisplifl.pdf.
{3}

LUSZTIG G. Some examples in square integrable representations of

semisimple p-adic groups [J]. Trans Amer Math Soc, 1983, 277:

623-653.
{4}

SHI J Y. The Kazhdan-Lusztig cells in certain affine Weyl groups

[M]. Berlin: Springer-Verlag, 1986.
{5}

KAC V. Infinite Dimensional Groups with Applications [M]. New York:

Springer-Verlag, 1985.
{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}

SHI J Y. A survey on the cell theory of affine Weyl groups [J].

Advances in Science of China, 1990, Math 3: 79-98.
{8}

GREENE C. Some partitions associated with a partially ordered set

[J]. J Comb Theory A, 1976, 20: 69-79.

施引文献

资源附件(0)

访问统计