Unitary dual

Summary

The unitary dual $\widehat{G}$ of a locally compact group $G$ is the set of equivalence classes of irreducible unitary representations of $G$. It usually carries the Fell topology. It is the space on which a "Fourier transform" of functions on $G$ lives. For abelian groups it is the Pontryagin dual, a group again. For nonabelian groups it is only a topological space, often non-Hausdorff. Determining it for a given group is a central problem of representation theory.