We study the canonical U(n-)-valued differential form, whose projections to
different Kac-Moody algebras are key ingredients of the hypergeometric integral
solutions of KZ-type differential equations and Bethe ansatz constructions. We
explicitly determine the coefficients of the projections in the simple Lie
albegras A_r, B_r, C_r, D_r in a conviniently chosen Poincare-Birkhoff-Witt
basis. As a byproduct we obtain results on the combinatorics of rational
functions, namely non-trivial identities are proved between certain rational
functions with partial symmetries.Comment: More typos correcte
