Functors for genuine representations of the metaplectic group and graded affine hecke algebras

In a recent pre-print, Ciubotaru and Trapa defi ned a family of exact functors carrying spherical Harish-Chandra modules for real classical linear algebraic groups to representations of a certain algebra called the graded affine Hecke algebra. Representations of this algebra can then be translated, thanks to results of Lusztig, Barbasch, and Moy, into representations of a p-adic group of the same type as the original real group. The result, in eff ect, is a Lefschetz functor for real classical linear algebraic groups; it also embeds the spherical unitary dual for the real group into the spherical unitary dual for the p-adic group. This thesis develops an analagous functor for genuine representations of the real and p-adic metaplectic groups.