论文标题
来自矢量值乘法功能的免费组表示，iii
Free group representations from vector-valued multiplicative functions, III
论文作者
论文摘要
让$π$是有限生成的非阿布尔自由组$γ$的不可约的统一表示；假设$π$在常规表示中薄弱。在2001年，第一和第三作者猜想这样的表示必须是奇怪的，单调的或重复的。在2004年，他们介绍了乘法表示的类别：这是通过查看其Cayley图上$γ$的动作而获得的一大批表示形式。 在本系列的第二篇论文中，我们表明了一些乘法表示是单调的。在这里，我们表明所有其他乘法表示都是奇数或偶然的。因此，为乘法表示建立了猜想。
Let $π$ be an irreducible unitary representation of a finitely generated nonabelian free group $Γ$; suppose $π$ is weakly contained in the regular representation. In 2001 the first and third authors conjectured that such a representation must be either odd or monotonous or duplicitous. In 2004 they introduced the class of multiplicative representations: this is a large class of representations obtained by looking at the action of $Γ$ on its Cayley graph. In the second paper of this series we showed that some of the multiplicative representations were monotonous. Here we show that all the other multiplicative representations are either odd or duplicitous. The conjecture is therefore established for multiplicative representations.
