论文标题
可数组的plancherel公式
The Plancherel formula for countable groups
论文作者
论文摘要
我们讨论了可计数组的plancherel公式，该公式将这种组$γ$定期表示的规范分解为直接的因子表示。我们的主要结果通过$γ$的Fc-Center $γ_ {\ rm fc} $的plancherel公式进行了对这种分解的精确描述（也就是说，即$γ$的正常sugbroup由$γ$组成的元素由带有有限偶有性类别的元素组成）；此描述涉及$γ_ {\ rm fc} $的合适完全断开的紧凑型自动形态的紧凑型组的动作。作为应用程序，我们确定线性组的plancherel公式。在附录中，我们使用Plancherel公式为Thoma's和Kaniuth定理提供统一的证明，这些证明分别表征了I型和常规表示II型的可数组。
We discuss a Plancherel formula for countable groups, which provides a canonical decomposition of the regular representation of such a group $Γ$ into a direct integral of factor representations. Our main result gives a precise description of this decomposition in terms of the Plancherel formula of the FC-center $Γ_{\rm fc}$ of $Γ$ (that is, the normal sugbroup of $Γ$ consisting of elements with a finite conjugacy class); this description involves the action of an appropriate totally disconnected compact group of automorphisms of $Γ_{\rm fc}$. As an application, we determine the Plancherel formula for linear groups. In an appendix, we use the Plancherel formula to provide a unified proof for Thoma's and Kaniuth's theorems which respectively characterize countable groups which are of type I and those whose regular representation is of type II.
