Abstract.  

The unitary dual of a reductive Lie group is a fundamental, yet hard and mysterious open problem. The complete answer is known only for some families (for example, for finite and compact groups, as well as the general linear groups GL(n,R)), and some small examples of real Lie groups. A parametrization of all irreducible representations is known, so the problem is to determine which of them are unitary.

Susana Salamanca-Riba has solved the problem for a certain important
collection of representations, those with “strongly regular infinitesimal character”, for any reductive Lie group. The goal of this talk is to explain this result, and to report on progress towards extending the result, in the case of the metaplectic group, to a slightly larger collection of representations, which we call “omega-regular”.