  J.~Sekiguchi determined the semisimple symmetric pairs (g,h), called nice
symmetric pairs, on which there is no non-zero invariant eigendistribution with
singular support. On such pairs, we study regularity of invariant distributions
annihilated by a polynomial of the Casimir operator. We deduce that invariant
eigendistributions on (gl(4,R),gl(2,R)*gl(2,R)) are locally integrable
functions.
