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).
Classification :
22E45, 22E46
Mots-clés :
Dual pairs, orbital integrals
Affiliations des auteurs :
Florent Bernon
1
;
Tomasz Przebinda
2
1
Dép. de Mathématiques, Université de Versailles, 78035 Versailles, France
2
Dept. of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A.
Florent Bernon; Tomasz Przebinda. Normalization of the Cauchy Harish-Chandra Integral. Journal of Lie Theory, Tome 21 (2011) no. 3, pp. 615-702. http://geodesic.mathdoc.fr/item/JOLT_2011_21_3_a1/
@article{JOLT_2011_21_3_a1,
author = {Florent Bernon and Tomasz Przebinda},
title = {Normalization of the {Cauchy} {Harish-Chandra} {Integral}},
journal = {Journal of Lie Theory},
pages = {615--702},
year = {2011},
volume = {21},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2011_21_3_a1/}
}
TY - JOUR
AU - Florent Bernon
AU - Tomasz Przebinda
TI - Normalization of the Cauchy Harish-Chandra Integral
JO - Journal of Lie Theory
PY - 2011
SP - 615
EP - 702
VL - 21
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2011_21_3_a1/
ID - JOLT_2011_21_3_a1
ER -
%0 Journal Article
%A Florent Bernon
%A Tomasz Przebinda
%T Normalization of the Cauchy Harish-Chandra Integral
%J Journal of Lie Theory
%D 2011
%P 615-702
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2011_21_3_a1/
%F JOLT_2011_21_3_a1
