On the middle convolution of local systems. With an Appendix by M.   Dettweiler and S. Reiter
  We study the middle convolution of local systems and realize special linear groups as Galois groups over the rationals. In the Appendix to this paper, written jointly with Stefan Reiter, we prove the existence of a new motivic local system with $G_2$-monodromy. 
Michael Dettweiler