Construction of Covering groups

Following McNamara we describe n-fold covers of a split reductive group. We discuss splitting properties of these covers when restricted to unipotent and maximal compact subgroups. Since inverse image of a maximal torus is a Heisenberg group, we parametrise its (genuine) representations by their (genuine) central characters. Then we define principal series representation and study spherical vectors in these representation. Reference:- Peter McNamara; Principal Series Representations of Metaplectic Groups Over Local Fields. Multiple Dirichlet Series, L-functions and Automorphic Forms, Birkhauser Progress in Math. 300 (2012) 299–327.