Coupled Painlev\'e VI systems in dimension four with affine Weyl group   symmetry of type $E_6^{(2)}$
  We find a four-parameter family of coupled Painlev\'e VI systems in dimension four with affine Weyl group symmetry of type $E_6^{(2)}$. This is the first example which gave higher order Painlev\'e type systems of type $E_{6}^{(2)}$. We study its symmetry and holomorphy conditions. 
Yusuke Sasano