Abstract
We study orbital integrals and invariant eigendistributions for the symmetric pair ( g , h ) = ( g l ( 4 , R ) , g l ( 2 , R ) × g l ( 2 , R ) ) . Let q = g / h and let N be the set of nilpotents of q . We first obtain an asymptotic behavior of orbital integrals around nonzero semisimple elements of q . We study eigendistributions around such elements and give an explicit basis of eigendistributions on q − N given by a locally integrable function on q − N .
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