Irreducible genuine characters of the Metaplectic group: Kazhdan-Lusztig algorithm and Vogan duality

We establish a Kazhdan-Lusztig algorithm to compute characters of irreducible genuine representations of the (nonlinear) metaplectic group with half-integral infinitesimal character. We then prove a character multiplicity duality theorem for representations of Mp(2n, ℝ) at fixed half-integral infinitesimal character. This allows us to extend some of Langlands' ideas to Mp(2n, ℝ).