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Combinatorics of Rational Functions and Poincaré- Birchoff-Witt Expansions of the Canonical U(n_)-Valued Differential Form
R. Rimányi1, L. Stevens2, and A. Varchenko1
1Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250 Phillips Hall, Chapel Hill, NC 27599, USA
{rimanyi, anv}@email.unc.edu
2Department of Mathematics, Universita' di Roma “La Sapienza”, 00198 Rome, Italy
stevens@mat.uniroma1.it
Annals of Combinatorics 9 (1) p.57-74 March, 2005
AMS Subject Classification: 33C67
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 Ar, Br, Cr, Dr in a conveniently chosen Poincaré- Birchoff-Witt basis.
Keywords: canonical differential form, KZ equation, Bethe ansatz, PBW-expansion, symmetric rational functions

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