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Combinatorics of rational functions and Poincare-Birkhoff-Witt expansions of the canonical U(n-)-valued differential form | | R. Rimanyi
; L. Stevens
; A. Varchenko
; | | Date: |
7 Jul 2004 | | Subject: | Combinatorics; Mathematical Physics; Representation Theory MSC-class: 33C67 | math.CO math-ph math.MP math.RT | | 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 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. | | Source: | arXiv, math.CO/0407101 | | Services: | Forum | Review | PDF | Favorites | |
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