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Abstract: Determining the irreducible "unitary" representations of a reductive group, the so-called unitary dual is one of the outstanding problems in harmonic analysis. (Unitary representations are the ones which seems to most likely occur "in nature" and which also form the "building blocks" for other such representations.) For many groups, such as the group SL(2,F) of 2x2 matrices over a real or p-adic field F, the unitary dual has been known for quite a while. Surprisingly, the unitary dual of the closely related (but non-reductive) n-fold metaplectic covering group G of SL(2,F) has not been completely described. In the p-adic case when p does not divide n, the unitary "principal series" representations were explicitly described by C. Moen in his PhD thesis, and in later unpublished work, using a model which turned out to be very complicated computationally. A similar idea was used by Ariturk to describe the "complementary series" in the case n=3, p>3. In this talk, we describe how more recent work of Flicker and Kazhdan allows one to extend the main results of Moen and Ariturk to the case of all p and all n, more-or-less finishing off the description of the unitary dual of G.