The cells in the weighted Coxeter group (C_n,l_m)
The cells in the weighted Coxeter group (C_n,l_m)
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加权 Coxeter 组中的单元格 (C_n,l_m)
DOI：
10.1016/j.jalgebra.2015.06.044
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发表时间：
2015
影响因子：
0.9
通讯作者：
时俭益
中科院分区：
文献类型：
--
作者：
时俭益
The affine Weyl group. $(\widetilde{C}_n,S)$ can be realized as the fixed point set of the. affine Weyl group $(\widetilde{A}_m,\widetilde{S}_m)$, $m\in\{2n-1,2n,2n+1\}$, under a certain group. automorphism $\alpha_{m,n}$.. Let $\widetilde{\ell}_m$ be the length. function of $\widetilde{A}_m$. The aim of the present paper is to give.a combinatorial description for all the left cells of.$\widetilde{A}_m$ which have non-empty intersection with.$\widetilde{C}_n$.. Then we use this description to deduce some formulae for the number of left cells of.the weighted Coxeter group $(\widetilde{C}_n,\widetilde{\ell}_m)$ in.the set $E_\lambda$ associated to any partition $\lambda$ of $m+1$.
The affine Weyl group. $(\widetilde{C}_n,S)$ can be realized as the fixed point set of the. affine Weyl group $(\widetilde{A}_m,\widetilde{S}_m)$, $m\in\{2n-1,2n,2n+1\}$, under a certain group. automorphism $\alpha_{m,n}$.. Let $\widetilde{\ell}_m$ be the length. function of $\widetilde{A}_m$. The aim of the present paper is to give.a combinatorial description for all the left cells of.$\widetilde{A}_m$ which have non-empty intersection with.$\widetilde{C}_n$.. Then we use this description to deduce some formulae for the number of left cells of.the weighted Coxeter group $(\widetilde{C}_n,\widetilde{\ell}_m)$ in.the set $E_\lambda$ associated to any partition $\lambda$ of $m+1$.