Geodesic
Derivatives of Elliptic Orbital Integrals on a Symplectic Space
Journal of Lie theory, Tome 30 (2020) no. 2, pp. 489-512
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For a real reductive dual pair with one member compact we study the orbital integrals on the corresponding symplectic space that occur in the Weyl-Harish-Chandra integration formula on that space. We obtain estimates of the derivatives of such integrals. These estimates are needed for expressing the intertwining distribution attached to a pair of representations in Howe's correspondence in terms of the orbital integrals. This is in analogy to Harish-Chandra's theory, where the distribution character of an irreducible admissible representation of a real reductive group factors through the semisimple orbital integrals on the group.
Classification : 22E45, 22E46, 22E30
Mots-clés : Reductive dual pairs, Howe duality, Weyl calculus, Lie superalgebras 
@article{JLT_2020_30_2_JLT_2020_30_2_a11,
     author = {M. McKee and A. Pasquale and T. Przebinda},
     title = {Derivatives of {Elliptic} {Orbital} {Integrals} on a {Symplectic} {Space}},
     journal = {Journal of Lie theory},
     pages = {489--512},
     year = {2020},
     volume = {30},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a11/}
}
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M. McKee; A. Pasquale; T. Przebinda. Derivatives of Elliptic Orbital Integrals on a Symplectic Space. Journal of Lie theory, Tome 30 (2020) no. 2, pp. 489-512. http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a11/