论文标题
Coxeter组的Poincaré系列双固定代表
Poincaré series of double coset representatives of Coxeter groups
论文作者
论文摘要
令$（W，S）$为有限排名的Coxeter系统，让$ J，K \ subset S $。我们研究了$ w $ $（w_j，w_k）$的最小长度代表的庞加莱系列的合理性：$ w $：我们得出的结论是，这主要取决于庞加尔派康卡雷（Poincaré）的合理性。对于仿射韦伊尔组，我们证明所有这些系列都是理性的，我们提供了一些明确的例子。
Let $(W,S)$ be a Coxeter system of finite rank and let $J,K\subset S$. We study the rationality of the Poincaré series of the set of representatives of minimal length of $(W_J,W_K)$-double cosets of $W$: we conclude that it depends mostly on the rationality of the Poincaré series of the normalizers of finite parabolic subgroups of $W$. For affine Weyl groups, we prove that all these series are rational and we give some explicit examples.
