Distributions propres invariantes sur la paire sym\' etrique (gl(4,R),gl(2,R)*gl(2,R))
arXiv:1102.0963
Abstract
We study orbital integrals and invariant eigendistributions for the symmetric pair (g,h)=(gl(4,R),gl(2,R)*gl(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.
arXiv comment79 pages, Submitted for publication