Categories of (g, sl_2))-modules (Please note the change of time!)

Let g be a complex semisimple Lie algebra and k \subset g be a subalgebra isomorphic to sl_2. Admissible (g,k)-modules are an interesting class of generalized Harish-Chandra modules, and are not part of Harish-Chandra module theory unless g has rank 2. One way to construct admissible (g,k)-modules is to apply the Zuckerman functor to a suitable thick parabolic category \tilde{O}_p. Zuckerman and I conjectured in 2012 that, under a certain restriction on the k-weights of modules in \tilde{O}_\p, the Zuckerman functor is an equivalence of the respective part of the category  \tilde{O}_\p with the category of admissible (g,k)- modules satisfying a certain lower bound on the minimal k-type. Serganova, Zuckerman and I recently proved this conjecture, and I will report on the main ideas of the proof.