Abstract: The most fundamental unsolved problem in the representation theory of Lie groups is the problem of the unitary dual: given a reductive Lie group G, can we parameterize the set of irreducible unitary G-representations? The Orbit Method suggests a correspondence between irreducible unitary G-representations and coverings of co-adjoint G-orbits. The main conceptual hurdle is *defining* this correspondence. In this talk, I will define it in the case when G is complex. Time permitting, I will explain how to generalize this correspondence for arbitrary G.
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