论文标题
代数组的字符在数字字段上
Characters of algebraic groups over number fields
论文作者
论文摘要
令$ k $为一个数字字段，$ \ mathbf {g} $一个代数组定义在$ k $上定义，$ \ mathbf {g}（k）$ $ k $ - rational点的组中的$ \ mathbf {g} $。 $ \ mathbf {g}（k）$由其独立元素生成。 An essential step in the proof is the classification of the $\mathbf{G}(k)$-invariant ergodic probability measures on an adelic solenoid naturally associated to $\mathbf{G}(k);$ this last result is deduced from Ratner's measure rigidity theorem for homogeneous spaces of $S$-adic Lie groups.
Let $k$ be a number field, $\mathbf{G}$ an algebraic group defined over $k$, and $\mathbf{G}(k)$ the group of $k$-rational points in $\mathbf{G}.$ We determine the set of functions on $\mathbf{G}(k)$ which are of positive type and conjugation invariant, under the assumption that $\mathbf{G}(k)$ is generated by its unipotent elements. An essential step in the proof is the classification of the $\mathbf{G}(k)$-invariant ergodic probability measures on an adelic solenoid naturally associated to $\mathbf{G}(k);$ this last result is deduced from Ratner's measure rigidity theorem for homogeneous spaces of $S$-adic Lie groups.
