Second level semi-degenerate fields in W3 Toda theory: matrix element   and differential equation
  In a recent study we considered W3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl3. We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules. 
Vladimir Belavin, Xiangyu Cao, Benoit Estienne and Raoul Santachiara
hep-th