Hilbert–Poincaré series for spaces of commuting elements in Lie groups
Hilbert–Poincaré series for spaces of commuting elements in Lie groups
复制标题
李群中通勤元素空间的希尔伯特-庞加莱级数
DOI：
10.1007/s00209-018-2122-1
复制
发表时间：
2017
影响因子：
0.8
通讯作者：
Mentor Stafa
中科院分区：
文献类型：
--
作者：
D. Ramras;Mentor Stafa
本文研究了李群中有序对交换元组空间的同调性。我们用g的Weyl群的不变量给出了这些空间的poincar<s:1>级数的显式公式。通过Bergeron和Silberman的工作，我们的结果也适用于，其中子群是自由群的下降中心级数中的项。最后，我们证明了Cohen-Stafa所研究的空间与其幂零类似物之间存在稳定的等价性。
In this article we study the homology of spacesof ordered pairwise commutingn-tuples in a Lie groupG. We give an explicit formula for the Poincaré series of these spaces in terms of invariants of the Weyl group ofG. By work of Bergeron and Silberman, our results also apply to, where the subgroupsare the terms in the descending central series of the free group. Finally, we show that there is a stable equivalence between the spacestudied by Cohen–Stafa and its nilpotent analogues.