Monodromy representations and Lyapunov exponents of origamis

Origamis are translation surfaces obtained by gluing finitely many unit squares and provide an easy access to Teichmller curves. In particular, their monodromy represenation can be explicitely determined. A general principle for the decomposition of this represenation is exhibited and applied to examples. Closely connected to it is a dynamical cocycle on the Teichmller curve. It is shown that its Lyapunov exponents, otherwise inaccessible, can be computed for a subrepresentation of rank two.