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J. reine angew. Math. 452 (1994), 163-217 Journal fur die reine und angewandte Mathematik
 

Summary: J. reine angew. Math. 452 (1994), 163-217 Journal fur die reine und
angewandte Mathematik
Walter de Gruyter
Berlin New York 1994
On the Fourier transforms of weighted
orbital integrals
By James Arthur*) at Toronto
Introduction
Suppose for a moment that G is a finite group. There are two canonical bases for the
vector space of class functions on G. One is parametrized by the set F(G) of conjugacy
classes in G, the other by the set 17(G) of (equivalence classes of) irreducible representa-
tions. Consider the elements of these bases as G-invariant linear functionals on C(G). In
other words, set
fG()= IG-1 E f(x-lx), ye(G),xEG
and
gO() =IGI-tr( E g(x)r(x)), 7 17(G),xeG
for functions f, g C(G). Then the two families of linear functionals satisfy inversion
formulas
(1) f(7) = E IG(y, r)fG(7r)incE(G)
and

  

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

 

Collections: Mathematics