Journal of Lie Theory 21 (2011), No. 3, 615--702
Copyright Heldermann Verlag 2011
Normalization of the Cauchy Harish-Chandra Integral
Florent Bernon
Dép. de Mathématiques, Université de Versailles, 78035 Versailles, France
Florent.Bernon@math.uvsq.fr
Tomasz Przebinda
Dept. of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A.
tprzebinda@gmail.com
This is the second of our three articles showing that the Cauchy Harish-Chandra integral maps invariant eigendistributions to invariant eigendistributions with the correct infinitesimal character. In this paper, we define a normalization of this integral for all real reductive dual pairs. Then we prove that the normalized Cauchy Harish-Chandra integral maps orbital integrals to orbital integrals for the pairs (Up,q, U1,1), (Op,q, Sp2(R)) and (Sp2n(R), O1,2).
Keywords: Dual pairs, orbital integrals.
MSC: 22E45; 22E46
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