Weyl chamber flow on irreducible quotients of products of PSL(2,R)

We study the topological dynamics of the action of the diagonal subgroup on quotients Gamma\PSL(2,R)PSL(2,R), where Gamma is an irreducible lattice. Closed orbits are described and a set of points of dense orbit is explicitly given. Such properties are expressed using the Furstenberg boundary of the symmetric space HH.