Combinatorics of rational functions and Poincare-Birkhoff-Witt expansions of the canonical U(n-)-valued differential form

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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.
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Combinatorics, Mathematical Physics, Representation Theory, 33C67

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http://salesiana.dossiersoluciones.com/handle/123456789/71800

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407101
 http://arxiv.org/abs/math/0407101

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arXiv