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

Irreducible Genuine Characters of the Metaplectic Group: Kazhdan-Lusztig Algorithm and Vogan Duality