Rigidity of monodromies for Appell's hypergeometric functions

Abstract

For monodromy representations of holonomic systems, the rigidity can be defined. We examine the rigidity of the monodromy representations for Appell's hypergeonietric functions, and get the representations explicitly. The results show how the topology of the singular locus and the spectral types of the local monodromies work for the study of the rigidity.