  We give an example of a Teichm\"uller curve which contains, in a factor of
its monodromy, a group which was not observed before. Namely, it has Zariski
closure equal to the group $SO^*(6)$ in its standard representation; up to
finite index, this is the same as $SU(3,1)$ in its second exterior power
representation.
  The example is constructed using origamis (i.e. square-tiled surfaces). It
can be generalized to give monodromy inside the group $SO^*(2n)$ for all $n$,
but in the general case the monodromy might split further inside the group.
  Also, we take the opportunity to compute the multiplicities of
representations in the (0,1) part of the cohomology of regular origamis,
answering a question of Matheus-Yoccoz-Zmiaikou.
