Lift of the Trivial Representation to a Nonlinear Double Cover

Let G be the nonlinear double cover of the real points of a connected, simply connected, semisimple complex group. In [16], we introduce a set of genuine small representations of G with infinitesimal character λ , denoted ∏ λ s (G). In this paper, we show that ρ 2s (\widetilde G) is precisely the set of genuine irreducible representations arising from the Kazhdan-Patterson lifting of the trivial representation, when G is simply laced and split.