Representaions of SL(2) over arithmetic Dedekind domains

Abstract

For describing automorphic forms of singular weight over number fields it is indispensable to understand therepresentations of groups like SL(2,O), where O is the ring of integers of a number field. Even for SL(2,Z)there are open questions. We report about recent progress on this problem for general arithmetic Dedekinddomains, and we discuss still open problems.