Geodesic
On the Tau Function for the Schlesinger Equation of Isomonodromic Deformations
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 184-191.

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

The tau function for the Schlesinger equation of isomonodromic deformations is represented as the result of successively applied elementary gauge transformations; this, in particular, suggests a simple proof for the Miwa theorem about the tau function. 
@article{MZM_2003_74_2_a1,
     author = {A. A. Bolibrukh},
     title = {On the {Tau} {Function} for the {Schlesinger} {Equation} of {Isomonodromic} {Deformations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {184--191},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a1/}
}
TY  - JOUR
AU  - A. A. Bolibrukh
TI  - On the Tau Function for the Schlesinger Equation of Isomonodromic Deformations
JO  - Matematičeskie zametki
PY  - 2003
SP  - 184
EP  - 191
VL  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a1/
LA  - ru
ID  - MZM_2003_74_2_a1
ER  - 
%0 Journal Article
%A A. A. Bolibrukh
%T On the Tau Function for the Schlesinger Equation of Isomonodromic Deformations
%J Matematičeskie zametki
%D 2003
%P 184-191
%V 74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a1/
%G ru
%F MZM_2003_74_2_a1
A. A. Bolibrukh. On the Tau Function for the Schlesinger Equation of Isomonodromic Deformations. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 184-191. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a1/

[1] Bolibrukh A. A., “Ob izomonodromnykh sliyaniyakh fuksovykh osobennostei”, Tr. MIAN, 221, Nauka, M., 1998, 127–142 | MR | Zbl

[2] Malgrange B., “Sur les déformations isomonodromiques. I: Singularités régulières”, Progr. Math., 37 (1983), 401–426 | MR | Zbl

[3] Bolibruch A. A., “On orders of movable poles of the Schlesinger equation”, J. Dynam. Control Systems, 6:1 (2000), 57–74 | DOI | MR

[4] Jimbo M., Miwa T., “Monodromy preserving deformations of linear ordinary differential equations, II”, Phys. D, 2 (1981), 407–448 | DOI | MR

[5] Okonek K., Shneider M., Shpindler Kh., Vektornye rassloeniya na kompleksnom proektivnom prostranstve, Mir, M., 1984 | Zbl

[6] Bolibruch A. A., “Vector bundles associated with monodromies and asymptotics of Fuchsian systems”, J. Dynam. Control Systems, 1:1 (1995), 229–252 | DOI | MR | Zbl