This article is cited in 1 paper

Rationality of the Knizhnik–Zamolodchikov equation solution

L. A. Sakhnovich


Abstract: We construct an explicit solution of the Knizhnik–Zamolodchikov system with $n=4$ and $m=2$ in the terms of hypergeometric functions. We prove that this solution is rational when the parameter $\rho$ is integer. We show that the Knizhnik–Zamolodchikov system has no rational solution in the case where $n=5$, $m=5$, and $\rho$ is integer.

Keywords: symmetric group, natural representation, Young tableau, integer eigenvalue.

Received: 10.10.2009

DOI: 10.4213/tmf6488

 English version: Theoretical and Mathematical Physics, 2010, 163:1, 472–478

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