Unipotent Representations of Real Groups

In 1980 Jim Arthur conjectured the existence of certainunipotent representations of reductive groups over local fields,which should play a fundamental role in the study of automorphicforms. Arthur did not give a definition of these representations(only some properties), and they are still not well understood,even in the case of Archimedean fields. I will discuss progress onthe case of the real field. An aspect of this is the Atlas of LieGroups and Representations, which is asoftware project to, amongother things, understand unipotent representations and the unitarydual of real reductive groups.