MONODROMY REPRESENTATIONS ASSOCIATED WITH THE GAUSS HYPERGEOMETRIC FUNCTION USING INTEGRALS OF A MULTIVALUED FUNCTION

Abstract

Monodromy representations on the space of solutions of the Gauss hypergeometric equation are studied by using integrals of a multivalued function. We first establish the fact that any solution of the Gauss hypergeometric equation is expressed by the integral of a multivalued function. Second, we give a necessary and sufficient condition for the irreducibility. Third, we realize the representations in the reducible cases. In the reducible cases, the exponents of the integrand do not satisfy the genericity condition and chains which are not necessarily cycles are needed to give a basis of the solution space. Finally, we give a complete list of finite reducible representations.