Kohno systems on Manin--Schechtman configuration spaces
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 2, Tome 46 (2012), pp. 120-128.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider multidimensional Fuchsian linear differential equations on the Manin–Schechtman configuration spaces, obtained by the Kohno construction. We study integrability of these systems in the sense of Frobenius and some of their reductions.
@article{CMFD_2012_46_a5,
     author = {V. P. Leksin},
     title = {Kohno systems on {Manin--Schechtman} configuration spaces},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {120--128},
     publisher = {mathdoc},
     volume = {46},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2012_46_a5/}
}
TY  - JOUR
AU  - V. P. Leksin
TI  - Kohno systems on Manin--Schechtman configuration spaces
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2012
SP  - 120
EP  - 128
VL  - 46
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2012_46_a5/
LA  - ru
ID  - CMFD_2012_46_a5
ER  - 
%0 Journal Article
%A V. P. Leksin
%T Kohno systems on Manin--Schechtman configuration spaces
%J Contemporary Mathematics. Fundamental Directions
%D 2012
%P 120-128
%V 46
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2012_46_a5/
%G ru
%F CMFD_2012_46_a5
V. P. Leksin. Kohno systems on Manin--Schechtman configuration spaces. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 2, Tome 46 (2012), pp. 120-128. http://geodesic.mathdoc.fr/item/CMFD_2012_46_a5/

[1] Leksin V. P., “Izomonodromnye deformatsii i sistemy Zhordana–Pokhgammera”, Uravneniya Penleve i smezhnye voprosy, Tezisy dokl. mezhd. konf. (Institut Eilera POMI RAN, Sankt-Peterburg), SPb., 2011, 104–107

[2] Leksin V. P., “Golomorfnye resheniya uravnenii izomonodromnoi deformatsii”, Progress v nelineinoi dinamike, Tezisy mezhd. konf., posv. 100-letiyu so dnya rozhdeniya A. A. Andronova, v. 1, 2002, 290–295 | MR

[3] Aguirre L., Felder G., Veselov A., “Gaudin subalgebras and stable rational curves”, Compos. Math., 147:5 (2011), 1463–1478 | DOI | MR | Zbl

[4] Kapovich M., Millson J., “Quantization of bending deformations of polygons in $\mathbb E^3$, hypergeometric integrals and the Gassner representation”, Canad. Math. Bull., 44 (2001), 36–60 | DOI | MR | Zbl

[5] Kapranov M., Voevodsky V., “Braided monoidal 2-categories and Manin–Schechtman higher braid groups”, J. Pure Appl. Algebra, 92 (1994), 241–267 | DOI | MR | Zbl

[6] Kohno T., “Integrable connections related to Manin and Schechtman's higher braid groups”, Illinois J. Math., 34 (1990), 476–484 | MR | Zbl

[7] Kohno T., “Linear representations of braid groups and classical Yang–Baxter equations”, Contemp. Math., 78 (1988), 339–363 | DOI | MR | Zbl

[8] Lawrence R., A presentation for Manin and Schechtman's higher braid groups, Preprint, 04129-91, MRSI, 1991

[9] Levelt A. H. M., “Hypergeometric functions”, Indag. Math., 23 (1961), 361–401 | MR

[10] Manin Yu. I., Schechtman V. V., “Arrangements of hyperplanes, higher braid groups and higher Bruhat orders”, Adv. Stud. Pure Math., 17 (1989), 289–308 | MR | Zbl

[11] Neretin Yu. A., On topologies on Lie braid groups, 2010, arXiv: 1006.1101v2

[12] Varchenko A., Special functions, KZ type equations, and representation theory, CBMS-NSF Regional Conf. Ser. in Appl. Math., 98, 2003 | MR | Zbl