Abstract:
 A fundamental problem in representation theory is to determine the unitary dual of a reductive Lie group G, namely the collection of equivalent classes of all irreducible unitary representations of G. For a compact Lie group, irreducible unitary representations were classified long time ago through the work of Cartan and Weyl. Unfortunately if G is not compact, its irreducible unitary representations are either 1dimensional or can only be found in infinite dimensional spaces. Thus a major task is to invent new ways of constructing unitary representations. In this talk, I will discuss some of these constructions, with a special emphasis on classical groups and their singular unitary representations.
