I suggest to define the KZ equations for exterior forms. As the KZ connection is flat, we have $d \circ d=0$ so that we can define a cohomology for KZ equations. Morover, we can define the KZ equations for an exterior form $w$:

$dw = \sum T(ij) (d log(z_i - z_j)) \wedge w$

the sum is taken for $i \neq j$ and $T(ij)$ are endormorphisms defined in the tensor products of a vector space $V$ (see Kassel, Quantum Groups, Springer Verlag).

Can we define the KZB equations for forms?