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JOURNAL OF FUNCTIONAL ANALYSIS 84, 19-84 (1989) Intertwining Operators and Residues

Summary: JOURNAL OF FUNCTIONAL ANALYSIS 84, 19-84 (1989)
Intertwining Operators and Residues
I. Weighted Characters
Department of Mathematics, Toronto,
Ontario, Canada M5S 1A1
Communicated by Ralph S. Phillips
Received August 30, 1986
Contents. 1. Intertwining operators. 2. Normalization. 3. Real groups.
4. p-adic groups. 5. Standard representations.6. The distributions JM(7zi).7. The
distributions JM(7i,X). 8. Residues. 9. Proof of Proposition 9.1. 10. Changes of
contour. 11. The spaces Jif,.(G(F,)} and JUGfF,)). 12. The map din. Appendix.
Let G be a reductive algebraic group over a local field F of characteristic
0. Let n[G(F))denote the set of equivalence classes of irreducible represen-
tations of G(F).The irreducible characters
are linear functionals on 3^(G(F)),the Hecke algebra of G(F).They are
invariant, in the sense that
Characters are of course central to the harmonic analysis of G(F).They
also occur on the spectral side of the trace formula, in the case of the com-
pact quotient. In the general trace formula, the analogous terms come from


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


Collections: Mathematics