Geodesic
Rationality of the Knizhnik–Zamolodchikov equation solution
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 86-93 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 
@article{TMF_2010_163_1_a5,
     author = {L. A. Sakhnovich},
     title = {Rationality of {the~Knizhnik{\textendash}Zamolodchikov} equation solution},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {86--93},
     year = {2010},
     volume = {163},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a5/}
}
TY  - JOUR
AU  - L. A. Sakhnovich
TI  - Rationality of the Knizhnik–Zamolodchikov equation solution
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 86
EP  - 93
VL  - 163
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a5/
LA  - ru
ID  - TMF_2010_163_1_a5
ER  - 
%0 Journal Article
%A L. A. Sakhnovich
%T Rationality of the Knizhnik–Zamolodchikov equation solution
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 86-93
%V 163
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a5/
%G ru
%F TMF_2010_163_1_a5
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/

[1] P. I. Etingof, I. B. Frenkel, A. A. Kirillov Jr., Lectures on Representation Theory and Knizhnik–Zamolodchikov Equations, Math. Surv. Monogr., 58, AMS, Providence, RI, 1998 | DOI | MR | Zbl

[2] L. A. Sakhnovich, Rational solutions of Knizhnik–Zamolodchikov system, arXiv: math-ph/0609067

[3] L. A. Sakhnovich, Rational solutions of KZ equation, case $S_4$, arXiv:math.CA/0702404

[4] A. N. Varchenko, Comm. Math. Phys., 171:1 (1995), 99–137 | DOI | MR | Zbl

[5] L. A. Sakhnovich, Cent. Eur. J. Math., 6:1 (2008), 179–187 | DOI | MR | Zbl

[6] A. Chervov, D. Talalaev, Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence, arXiv: hep-th/0604128

[7] G. Felder, A. P. Veselov, Int. Math. Res. Not., 15 (2007), Art. ID rnm046, 21 | MR | Zbl

[8] L. A. Sakhnovich, Oper. Matrices, 1:1 (2007), 87–111 | DOI | MR | Zbl

[9] Jin-Quan Chen, Group Representation Theory for Physicists, World Sci., Singapore, 1989 | MR | Zbl

[10] Khamermesh M., Teoriya grupp i ee primenenie k fizicheskim problemam, Mir, M., 1966 | MR | Zbl

[11] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. T. 1. Gipergeometricheskaya funktsiya. Funktsii Lezhandra, Nauka, M., 1973 | MR | MR | Zbl

[12] L. A. Sakhnovich, Spectral Theory of Canonical Differential Systems. Method of Operator Identities, Operator Theory: Adv. Appl., 107, Birkhäuser, Basel, 1999 | MR | Zbl