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 Tr. Mat. Inst. Steklova, 2012, Volume 278, Pages 138–147 (Mi tm3399)

Multidimensional Jordan–Pochhammer systems and their applications

V. P. Leksin

Moscow State Regional Social-Humanitarian Institute, Kolomna, Moscow oblast, Russia

Abstract: We consider the so-called Jordan–Pochhammer systems, a special class of linear Pfaffian systems of Fuchsian type on complex linear (or projective) spaces. These systems appeared as systems of differential equations for hypergeometric type integrals in which the integrand is a product of powers of linear functions. These systems also arise in some reductions of the Knizhnik–Zamolodchikov equations. The main advantage of these systems is the possibility of presenting a basis in the solution space of such systems in an explicit integral form and, as a consequence, of describing their monodromy representation. The main focus in the paper is placed on the applications of Jordan–Pochhammer systems. We describe the relationship of Jordan–Pochhammer systems to isomonodromic deformations of Fuchsian systems that are described by the Schlesinger equations, as well as to the linearization of the dynamical system of bending spatial polygons. We also describe the application of Jordan–Pochhammer systems to constructing Kohno systems on the Manin–Schechtman configuration spaces.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 278, 130–138

Bibliographic databases:

Document Type: Article
UDC: 517.952+517.552

Citation: V. P. Leksin, “Multidimensional Jordan–Pochhammer systems and their applications”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 278, MAIK Nauka/Interperiodica, Moscow, 2012, 138–147; Proc. Steklov Inst. Math., 278 (2012), 130–138

Citation in format AMSBIB
\Bibitem{Lek12} \by V.~P.~Leksin \paper Multidimensional Jordan--Pochhammer systems and their applications \inbook Differential equations and dynamical systems \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2012 \vol 278 \pages 138--147 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3399} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3058790} \transl \jour Proc. Steklov Inst. Math. \yr 2012 \vol 278 \pages 130--138 \crossref{https://doi.org/10.1134/S0081543812060132} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309861500013} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84867338451} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. T. Yokoyama, “Multivariable Euler transform of systems of linear ordinary differential equations of Okubo normal form”, Ramanujan J., 42:1 (2017), 157–172
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