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Duality for Nonlinear Simply Laced Groups Jeffrey Adams

Summary: Duality for Nonlinear Simply Laced Groups
Jeffrey Adams
and Peter E. Trapa
One of the key tools in the study of character theory of real reductive groups
is Vogan duality, which relates representations of real forms of GC and rep-
resentations of real forms of G
C. Here GC is a connected complex reductive
algebraic group and G
C is its dual group. This duality is an aspect of the
Local Langlands conjecture in this setting. It is of interest to extend these
results to nonlinear groups. The purpose of this paper is to prove a version
of Vogan duality for nonlinear groups in the simply laced case.
1 Introduction
The goal of this paper is to extend some of the formalism of the Local Lang-
lands Conjecture to certain nonlinear (that is, nonalgebraic) double covers
of real groups. Such nonlinear groups, for example the two-fold cover of the
symplectic group, have long been known to play an interesting role in the
theory of automorphic forms of algebraic groups.
The Langlands formalism applies to the real points G of a connected,


Source: Adams, Jeffrey - Department of Mathematics, University of Maryland at College Park


Collections: Mathematics