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On a Family of Distributions obtained from Orbits

Published online by Cambridge University Press:  20 November 2018

James Arthur
James Arthur*
Affiliation:
University of Toronto, Toronto, Ontario
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Suppose that G is a reductive algebraic group defined over a number field F. The trace formula is an identity

of distributions. The terms on the right are parametrized by “cuspidal automorphic data”, and are defined in terms of Eisenstein series. They have been evaluated rather explicitly in [3]. The terms on the left are parametrized by semisimple conjugacy classes and are defined in terms of related G(A) orbits. The object of this paper is to evaluate these terms.

In previous papers we have already evaluated in two special cases. The easiest case occurs when corresponds to a regular semisimple conjugacy class in G(F). We showed in Section 8 of [1] that for such an , could be expressed as a weighted orbital integral over the conjugacy class of σ. (We actually assumed that was “unramified”, which is slightly more general.) The most difficult case is the opposite extreme, in which corresponds to {1}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 1 , 01 February 1986 , pp. 179 - 214
Copyright
Copyright © Canadian Mathematical Society 1986

References

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