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Lifting of Characters for Nonlinear Simply Laced Groups
 

Summary: Lifting of Characters for Nonlinear Simply
Laced Groups
Jeffrey Adams and Rebecca Herb
September 5, 2008
Abstract
One aspect of the Langlands program for linear groups is lifting of charac-
ters, 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 G
is a two-fold cover of a real reductive group G. The main result is that there
is an operation, denoted Lift
eG
G, taking a stable virtual character of G to 0 or
a virtual genuine character of G, and Lift
eG
G() may be explicitly computed
if is a stable sum of standard modules.
1 Introduction
The Langlands program is concerned with representation theory and auto-
morphic forms of algebraic (linear) groups. Suppose G is a nonlinear group,

  

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

 

Collections: Mathematics