Duality for nonlinear simply laced groups (Q2894210)

The authors extend Vogan's duality to a certain class of nonalgebraic groups. Vogan duality relates characters of representations of a real reductive group \(G\) with characters of representations of real forms of reductive subgroups of the complex Langlands dual group \(G^\vee_{{\textstyle\mathbb{C}}}\). The purpose of the present paper is to give a unified duality theory for all nonlinear double covers of simply laced real reductive groups, and to use this to extend some of the formalism of the local Langlands conjecture to such nonalgebraic groups. One key point is that the dual group plays no role.