Geodesic
Rationality of the~Knizhnik--Zamolodchikov equation solution
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 86-93

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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, integer eigenvalue.
Mots-clés : Young tableau 
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     author = {L. A. Sakhnovich},
     title = {Rationality of {the~Knizhnik--Zamolodchikov} equation solution},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {86--93},
     publisher = {mathdoc},
     volume = {163},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a5/}
}
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L. A. Sakhnovich. Rationality of the~Knizhnik--Zamolodchikov equation solution. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 86-93. http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a5/