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Induced Representations, Intertwining Operators and James Arthur

Summary: Induced Representations, Intertwining Operators and
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-
Shelstad-Kottwitz 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 self-intertwining 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-


Source: Arthur, James G. - Department of Mathematics, University of Toronto


Collections: Mathematics