  We study the canonical U(\n)-valued elliptic differential form, whose
projections to different Kac-Moody algebras are key ingredients of the
hypergeometric integral solutions of elliptic KZ differential equations and
Bethe ansatz constructions. We explicitly determine the coefficients of the
projections in the simple Lie algebras A_r, B_r, C_r, D_r in a conveniently
chosen Poincare-Birkhoff-Witt basis. As an application we give a new formula
for eigenfunctions of Hamiltonians of the Calogero-Moser model.
