Combinatorics of Rational Functions and Poincaré-
Birchoff-Witt Expansions of the Canonical
*U*(*n_*)-Valued Differential Form

R. Rimányi^{1}, L. Stevens^{2}, and A. Varchenko^{1}

{rimanyi, anv}@email.unc.edu

stevens@mat.uniroma1.it

Annals of Combinatorics 9 (1) p.57-74 March, 2005

Abstract:

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 algebras A_{r}, B_{r}, C_{r}, Dr in a conveniently chosen Poincaré-
Birchoff-Witt basis.

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