Hitchin connection on the Veech curve

We recall van Gemmen and de Jong's construction of a vector bundle with a (projectively) flat connection, called the Hitchin connection, over the moduli space of genus two curves. We pull back this (projectively) flat vector bundle to a Teichmueller curve which was discovered by Veech: We use the description of this curve given by Lochak. The parallel transport equation of this pulled back connection is an explicit ODE of Fuchsian type with regular singularities. A solution of this ODE is obtained in terms of iterated integrals. Using this solution, an explicit formula for the monodromy representation of the orbifold fundamental group of this Teichmueller curve is given.  This is partly with J. E. Andersen and N. L. Gammelgaard.