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Parabolic transfer for real groups

Author: James Arthur
Journal: J. Amer. Math. Soc. 21 (2008), 171-234
MSC (2000): Primary 22E30, 22E55
Published electronically: June 25, 2007
MathSciNet review: 2350054
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Abstract: We shall establish an identity between distributions on different real reductive groups. The distributions arise from the trace formula. They represent the main archimedean terms in both the invariant and stable forms of the trace formula. The identity will be an essential part of the comparison of these formulas. As such, it is expected to lead to reciprocity laws among automorphic representations on different groups.

Our techniques are analytic. We shall show that the difference of the two sides of the proposed identity is the solution of a homogeous boundary value problem. More precisely, we shall show that it satisfies a system of linear differential equations, that it obeys certain boundary conditions around the singular set, and that it is asymptotic to zero. We shall then show that any such solution vanishes.

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Additional Information

James Arthur
Affiliation: Department of Mathematics, University of Toronto, Bahen Centre, 6th Floor, 40 St George Street, Toronto, ON M5S 2E4 Canada

Received by editor(s): December 21, 2005
Published electronically: June 25, 2007
Additional Notes: The author was supported in part by NSERC Operating Grant A3483.
Article copyright: © Copyright 2007 American Mathematical Society

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