论文标题
sp（n，1）允许适当的1个循环为统一的表示形式
Sp(n,1) admits a proper 1-cocycle for a uniformly bounded representation
论文作者
论文摘要
我们验证了Shalom对任何n：I.E.我们证明它在Hilbert空间上的构成仿射作用的简单级别Lie Group Sp（n，1）的猜想。我们提供两个不同的证据。这两种方法都至关重要的是，迈克尔·考林（Michael Cowling）对统一的界限表示。第一种方法非常抽象：它使用Shalom的自动启示性结果，几乎不需要计算。第二种方法是明确的：我们从Sobolev嵌入的关键案例的非连续性中推断出共生的术语。这项工作灵感来自皮埃尔·朱格（Pierre Julg）在鲍姆（Baum）上的工作 - 康涅狄格州的猜想（n，1）。
We verify Shalom's conjecture for the simple real-rank-one Lie group Sp(n ,1) for any n: i.e. we show that it admits a metrically proper affine action on a Hilbert space whose linear part is a uniformly bounded representation. We provide two different proofs. Both approaches crucially use results on uniformly bounded representations by Michael Cowling. The first approach is quite abstract: it uses an automatic-properness result of Shalom and requires almost no computations. The second approach is explicit: we deduce the properness of cocycles from the non-continuity of a critical case of the Sobolev embedding. This work is inspired from Pierre Julg's work on the Baum--Connes conjecture for Sp(n,1).
