 
Summary: Contemporary Mathematics
Problems for Real Groups
James Arthur
To Bill Casselman and Dragan Milici´c
At the suggestion of Bill Casselman, I have tried to compile a set of interesting
problems 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 1
2. Endoscopic character identities 4
3. Orthogonality relations 6
4. Weighted orbital integrals 8
