 
Summary: Pure and Applied Mathematics Quarterly
Volume 2, Number 1
(Special Issue: In honor of
John H. Coates, Part 1 of 2)
199217, 2006
A Note on Lpackets
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 padic 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 Lpackets, since their constituents could
then be equipped with a common set of Lfunctions and factors, by the con
