Geodesic
Derivatives of Elliptic Orbital Integrals on a Symplectic Space
Mark McKee1 ; Angela Pasquale2 ; Tomasz Przebinda3
1338 Hammond Lane, Providence, UT 84332, U.S.A.
2Institut Elie Cartan de Lorraine, UMR CNRS 7502, Université de Lorraine, 57045 Metz, France
3Department of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A.
Journal of Lie Theory, Tome 30 (2020) no. 2, pp. 489-512

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Mark McKee  1   ; Angela Pasquale  2   ; Tomasz Przebinda  3

1 338 Hammond Lane, Providence, UT 84332, U.S.A.
2 Institut Elie Cartan de Lorraine, UMR CNRS 7502, Université de Lorraine, 57045 Metz, France
3 Department of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A. 
Mark McKee; Angela Pasquale; Tomasz 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/JOLT_2020_30_2_a11/
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     author = {Mark McKee and Angela Pasquale and Tomasz 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/JOLT_2020_30_2_a11/}
}
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