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Pure and Applied Mathematics Quarterly Volume 2, Number 1

Summary: Pure and Applied Mathematics Quarterly
Volume 2, Number 1
(Special Issue: In honor of
John H. Coates, Part 1 of 2)
199--217, 2006
A Note on L-packets
James Arthur
To John Coates on his sixtieth birthday
1. Introduction. Suppose that G is a connected reductive algebraic group over
a field F of characteristic 0. For example, we could take G to be the group SL(n)
of unimodular (n n)-matrices. We assume for a moment that F is any local
field. In other words, F is a finite extension of either the archimedean field R or
a nonarchimedean p-adic field Qp.
One of the fundamental problems of local harmonic analysis is to classify the set
(G) of equivalence classes of irreducible representations of G(F). The problem
separates naturally into two parts. The first is to establish the local Langlands
correspondence. This conjecture of Langlands asserts that (G) is a disjoint
union of finite subsets , indexed by (equivalence classes of) Langlands para-
meters for G. The sets are called L-packets, since their constituents could
then be equipped with a common set of L-functions and -factors, by the con-


Source: Arthur, James G. - Department of Mathematics, University of Toronto


Collections: Mathematics