Monodromy representations of hypergeometric systems with respect to fundamental series solutions

摘要

We study the monodromy representation of the generalized hypergeometricdifferential equation and that of Lauricella's $F_C$ system of hypergeometricdifferential equations. We use fundamental systems of solutions expressed bythe hypergeometric series. We express non-diagonal circuit matrices asreflections with respect to root vectors with all entries $1$. We present asimple way to obtain circuit matrices.