Arithmetic Groups arising as hypergeometric monodromy

Abstract: The simplest type of linear differential equations on one variable are the hypergeometric equations of type (n)F(n-1). The monodromy group associated to these is easy to describe thanks to a 1960 result of Levelt. Recently there has been interest in determining how big the monodromy group is (whether it is an arithmetic group etc). We give many examples where the monodromy group is arithmetic (these are the first examples of infinite families of monodromy groups) and also discuss when the monodromy group can be non-arithmetic.