Journal of Lie Theory

no. 3
Normalization of the Cauchy Harish-Chandra Integral
Journal of Lie Theory, Volume 21 (2011) no. 3, pp. 615-702
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).
DOI: 10.5802/jolt.643
Classification: 22E45, 22E46
Keywords: Dual pairs, orbital integrals 
@article{JOLT_2011_21_3_a1,
     author = {F. Bernon and T. Przebinda},
     title = {Normalization of the {Cauchy} {Harish-Chandra} {Integral}},
     journal = {Journal of Lie Theory},
     pages = {615--702},
     year = {2011},
     volume = {21},
     number = {3},
     doi = {10.5802/jolt.643},
     zbl = {1238.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.643/}
}
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%A T. Przebinda
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F. Bernon; T. Przebinda. Normalization of the Cauchy Harish-Chandra Integral. Journal of Lie Theory, Volume 21 (2011) no. 3, pp. 615-702. doi: 10.5802/jolt.643

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