PageHeader : Funkcialaj Ekvacioj, 40 (1997) 139-163 Title : Irreducibility of the Second and the Fourth Painleve Equations AuthorInfo : By AuthorInfo : Masatoshi NOUMI and Kazuo OKAMOTO AuthorInfo : (Kobe University and University of Tokyo, Japan) AuthorInfo : Dedicated to Professor Hikosaburo Komatsu on his sixtieth birthday section : Introduction section : 1. Invariant divisors for $\mathrm{H}_{\mathrm{I}\mathrm{I}}$ subsection : 1.1. Weight decomposition subsection : 1.2. Determination of the polynomial $G$ subsection : 1.3. Existence of invariant divisors section : 2. Invariant divisors for $\mathrm{H}_{\mathrm{I}\mathrm{V}}$ subsection : 2.1. Decomposition of the Hamiltonian vector field subsection : 2.2. The Kernel of the linear operator $P(\lambda, \mu)$ subsection : 2.3. Determination of the polynomial $G$ subsection : 2.4. Weyl chamber section : References