  Irrational conformal field theory (ICFT) includes rational conformal field
theory as a small subspace, and the affine-Virasoro Ward identities describe
the biconformal correlators of ICFT. We reformulate the Ward identities as an
equivalent linear partial differential system with flat connections and new
non-local conserved quantities. As examples of the formulation, we solve the
system of flat connections for the coset correlators, the correlators of the
affine-Sugawara nests and the high-level $n$-point correlators of ICFT.
