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Orbital Integrals on Forms of SL(3), II

Published online by Cambridge University Press:  20 November 2018

R. P. Langlands  and
D. Shelstad
R. P. Langlands
Affiliation:
Institute for Advanced Study, Princeton, New Jersey
D. Shelstad
Affiliation:
University of Utah, Salt Lake City, Utah
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In the paper [6] we described in a precise fashion the notion of transfer of orbital integrals from a reductive group over a local field to an endoscopic group. We did not, however, prove the existence of the transfer. This remains, indeed, an unsolved problem, although in [7] we have reduced it to a local problem at the identity.

In the present paper we solve this local problem for two special cases, the group SL(3), which is not so interesting, and the group SU(3), and then conclude that transfer exists for any group of type A2.The methods are those of [4], and are based on techniques of Igusa for the study of the asymptotic behavior of integrals on p-adic manifolds. (As observed in [7], the existence of the transfer over archimedean fields is a result of earlier work by Shelstad.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 3 , 01 June 1989 , pp. 480 - 507
Copyright
Copyright © Canadian Mathematical Society 1989

References

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