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Distributions propres invariantes sur la paire symétrique (gl(4,R)/gl(2,R)*gl(2,R))

Abstract : We look for invariant eigendistributions for the symmetric pair (gl (4, R) / gl (2, R) *gl (2, R)). For this, I first describe the semisimple orbits of this quotient under Gl(2,R)*Gl(2,R) action. I then generalize certain results on orbital integral of rank one (of J.Faraut) in the rank two. So I describe the behavior of the orbital integrals in the neighborhood of the semi-regular points. Then I study the invariant eigendistributions which are given by locally integrable functions. I thus determine all invariant eigenfunctions on the open dense set of regular elements. For this I use the expression of radial parts of invariant differential operators with constant coefficients in terms of Dunkl's operators. The behavior of the orbital integrals gives matching conditions on these functions to be invariant eigendistributions on the whole space without the nilpotents. We obtain a vectoriel space of dimension 6.
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Contributor : Nicolas Jacquet <>
Submitted on : Tuesday, February 1, 2011 - 1:00:35 PM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM
Long-term archiving on: : Monday, May 2, 2011 - 3:12:45 AM


  • HAL Id : pastel-00561472, version 1



Nicolas Jacquet. Distributions propres invariantes sur la paire symétrique (gl(4,R)/gl(2,R)*gl(2,R)). Théorie des groupes [math.GR]. Ecole Polytechnique X, 2010. Français. ⟨pastel-00561472⟩



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