turkmath.org

In various applications of automorphic forms it becomes crucial to know the finite dimensional representations of $SL_(2,O)$, where $O$ is a maximal order in a number field. There are amazingly open questions concerning these representations. But recently there has been some progress. In particular, we determined all linear characters of $SL(2,O)$ and we applied the general theory of Weil representations of locally compact abelian groups invented by Weil to generate interesting family of representations of $SL(2,O)$ which possibly contain all finite dimensional representations of $SL(2,O)$ of finite image.