幂零子群的相对性质（T）
Relative Property (T) for Nilpotent Subgroups
摘要：
证明了幂零正规子群的阿贝尔化的相对性质（T）蕴含着子群自身的相对性质（T）。这个结果和其他结果是一个独立定理的结果，该定理指出，如果$H$是局部紧群$G$的闭子群，并且$A$是$H$的中心的闭子群，使得$A$在$G$中正规，并且$(G/A, H/A)$具有相对性质（T），则$(G, H^{(1)})$具有相对性质（T），其中$H^{(1)}$是$H$的换位子群的闭包。事实上，$A$在$H$中心的假设可以用更弱的假设来代替，即$A$是阿贝尔的，并且$A$的酉对偶上的每个$H$ -不变有限测度都在不动点集上得到支持.
英文摘要：
We show that relative Property (T) for the abelianization of a nilpotent normal subgroup implies relative Property (T) for the subgroup itself. This and other results are a consequence of a theorem of independent interest, which states that if $H$ is a closed subgroup of a locally compact group $G$, and $A$ is a closed subgroup of the center of $H$, such that $A$ is normal in $G$, and $(G/A, H/A)$ has relative Property (T), then $(G, H^{(1)})$ has relative Property (T), where $H^{(1)}$ is the closure of the commutator subgroup of $H$. In fact, the assumption that $A$ is in the center of $H$ can be replaced with the weaker assumption that $A$ is abelian and every $H$-invariant finite measure on the unitary dual of $A$ is supported on the set of fixed points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
