 
Summary: Induced Representations, Intertwining Operators and
Transfer
James Arthur
This paper is dedicated to George Mackey.
Abstract. Induced representations and intertwining operators give rise to
distributions that represent critical terms in the trace formula. We shall de
scribe a conjectural relationship between these distributions and the Langlands
ShelstadKottwitz transfer of functions
Our goal is to describe a conjectural relationship between intertwining oper
ators and the transfer of functions. One side of the proposed identity is a linear
combination of traces
tr RP (w) IP (, f) ,
where IP (, f) is the value of an induced representation at a test function f, and
RP (w) is a standard selfintertwining operator for the representation. Distribu
tions of this sort are critical terms in the trace formula. The other side is defined
by the transfer of f to an endoscopic group. The endoscopic transfer of functions
represents a sophisticated theory, some of it still conjectural, for comparing trace
formulas on different groups [L2]. This is a central theme in the general study of
automorphic forms.
There are a number of relatively recent ideas of Langlands, Shelstad and Kot
