加权的~Coxeter~群~$\widetilde{\bmC}_{\bmn}$~的左胞腔
Keywords: 仿射~Weyl~群,左胞腔,拟分裂,加权的~Coxeter~群
Abstract:
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~$1\leqslantk\leqslant2n+1$.
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