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Invent. math. 97, 257-290 (1981) 1Springer-Verlag 1989
 

Summary: Invent. math. 97, 257-290 (1981)
1Springer-Verlag 1989
The L2-Lefschetznumbers of Hecke operators
James Arthur*
Department of Mathematics, University of Toronto, Toronto, Canada
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 1. Hecke operators and L2-cohomology . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .52. The spectral decomposition of cohomology
. . . . . . . . . . . . . . . . . . . . . . . . .6 3. Application of the trace formula
54. The functions 'PA,T). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 5. Proof of Theorem 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. The main formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction
Suppose that G is a semisimple Lie group and that F is a discrete subgroup
of G. We assume that F is an arithmetic subgroup defined by congruence condi-
tions, and for simplicity, suppose also that G is contained in a simply connected
complex group. A fundamental problem is to decompose the regular representa-

  

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

 

Collections: Mathematics