Lifting of Characters for Nonlinear Simply Laced Groups

One aspect of the Langlands program for linear groups is lifting of characters, which relates virtual representations on a group G with those on an endoscopic group for G. The goal of this paper is to extend this theory to nonlinear two-fold covers of real groups in the simply laced case. Suppose G̃ is a two-fold cover of a real reductive group G. The main result is that there is an operation, denoted Lift e G G, taking a stable virtual character of G to 0 or a virtual genuine character of G̃, and Lift e G G(Θπ) may be explicitly computed if π is a stable sum of standard modules.