Construction of systems of differential equations of Okubo normal form with rigid monodromy

For systems of differential equations of the form (xI(n) - T)dy/dx = Ay (systems of Okubo normal form), where A is an n x n constant matrix and T is an n x n constant diagonal matrix, two kinds of operations (extension and restriction) are defined. It is shown that every irreducible system of Okubo normal form of semi-simple type whose monodromy representation is rigid is obtained from a rank 1 system of Okubo normal form by a finite iteration of the operations. Moreover, an algorithm to calculate the generators of monodromy groups for rigid systems of Okubo normal form is given. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.