Lift of the Trivial Representation to a Nonlinear Double Cover.

Let |$\widetilde G$| 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 |$\widetilde G$| with infinitesimal character |$\lambda $|⁠ , denoted |$\prod _\lambda ^s (\widetilde G)$|⁠. In this paper, we show that |$\prod _{\rho /2} ^s (\widetilde G)$| is precisely the set of genuine irreducible representations arising from the Kazhdan–Patterson lifting of the trivial representation, when |$\widetilde G$| is simply laced and split. [ABSTRACT FROM AUTHOR]