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L-Indistinguishability For SL (2)

Published online by Cambridge University Press:  20 November 2018

J-P. Labesse  and
R. P. Langlands
J-P. Labesse
Affiliation:
Faculté des Sciences, Dijon, France
R. P. Langlands
Affiliation:
The Institute for Advanced Study, Princeton, New Jersey
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The notion of L-indistinguishability, like many others current in the study of L-functions, has yet to be completely defined, but it is in our opinion important for the study of automorphic forms and of representations of algebraic groups. In this paper we study it for the simplest class of groups, basically forms of SL(2). Although the definition we use is applicable to very few groups, there is every reason to believe that the results will have general analogues [12].

The phenomena which the notion is intended to express have been met–and exploited–by others (Hecke [5] § 13, Shimura [17]). Their source seems to lie in the distinction between conjugacy and stable conjugacy. If F is a field, G a reductive algebraic group over F, and the algebraic closure of F then two elements of G(F) may be conjugate in without being conjugate in G(F).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 4 , 01 August 1979 , pp. 726 - 785
Copyright
Copyright © Canadian Mathematical Society 1979

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