  We give an expression for the pull back of the Hitchin connection from the
moduli space of genus two curves to a ten-fold covering of a Teichm\"uller
curve discovered by Veech. We then give an expression, in terms of iterated
integrals, for the monodromy representation of this connection. As a corollary
we obtain quantum representations of infinitely many pseudo-Anosov elements in
the genus two mapping class group.
