 
Summary: PROBLEMS FOR REAL GROUPS
James Arthur*
At the suggestion of Bill Casselman, I have tried to compile a set of interesting prob
lems for real groups. I have not made any attempt to represent the field as a whole. Some
of the problems are in fact quite idiosyncratic. They all come from real harmonic analysis,
and are generally motivated by global questions in automorphic forms.
The list was put together rather quickly, and could certainly stand further reflection.
I expect that I have overlooked some points, and have perhaps misstated others. The
problems should be treated as guidelines, to be reshaped as necessary in any attempts to
solve them.
Unless otherwise indicated, G will denote a connected, reductive algebraic group over
R in the discussion below.
Contents
§1 Endoscopic transfer
§2 Endoscopic character identities
§3 Orthogonality relations
§4 Weighted orbital integrals
§5 Intertwining operators and residues
§6 Twisted groups
§7 Traces of intertwining operators
