A class of higher order Painleve systems arising from integrable hierarchies of type A

A relationship between Painleve systems and infinite-dimensional integrable hierarchies is studied. We derive a class of higher order Painleve systems from Drinfeld-Sokolov (DS) hierarchies of type A by similarity reductions. This result allows us to understand some properties of Painleve systems, Hamiltonian structures, Lax pairs and affine Weyl group symmetries.