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On Twisted Orbital Integral Identities for PGL(3) Over A p-adic Field

Published online by Cambridge University Press:  20 November 2018

David Joyner
David Joyner*
Affiliation:
Department of Mathematics, U.S. Naval Academy, Annapolis, MD 21402
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Abstract

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The object of this paper is to prove certain p-adic orbital integral identities needed in order to accomplish the symmetric square transfer via the twisted Arthur trace formula. Only §5 of this article contains original material, the rest of it is due to R. Langlands. Very briefly, we reduce the problem of proving certain orbital integral identities for “matching” functions in the respective Hecke algebras to two counting problems on the buildings. We give Langlands’ solution of one of these problems in the case of the unit elements of the respective Hecke algebras and §5 provides the solution to the other one, again, in the unit element case. The main results assume p ≠ 2.

Keywords

11F7011R3922E50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 6 , 01 December 1990 , pp. 1098 - 1130
Copyright
Copyright © Canadian Mathematical Society 1990

Footnotes

Partially supported by an NSF fellowship.

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