论文标题
在本地领域的代数群体的统一表示
On unitary representations of algebraic groups over local fields
论文作者
论文摘要
令$ \ mathbf {g} $为特征零的本地字段$ \ mathbf k $上的代数组。我们表明，由$ \ Mathbf k $ - $ \ mathbf g $组成的局部紧凑型组$ \ mathbf g（\ mathbf k）$是I类型I的$ \ Mathbf k $ - rational点。 $ \ mathbf g（\ mathbf k）$是Deitmar和van Dijk最近研究的跟踪类。
Let $\mathbf{G}$ be an algebraic group over a local field $\mathbf k$ of characteristic zero. We show that the locally compact group $\mathbf G(\mathbf k)$ consisting of the $\mathbf k$-rational points of $\mathbf G$ is of type I. Moreover, we complete Lipsman's characterization of the groups $\mathbf G$ for which every irreducible unitary representation of $\mathbf G(\mathbf k)$ is a CCR representation and show at the same time that such groups $\mathbf G(\mathbf k)$ are trace class as studied recently by Deitmar and van Dijk.
