DESSINS D'ENFANTS AND DIFFERENTIAL EQUATIONS

Описание

Тип публикации: статья из журнала

Год издания: 2008

Идентификатор DOI: 10.1090/S1061-0022-08-01033-9

Ключевые слова: Riemann-Hilbert problem, Fuchsian equation, dessins d'enfants, Dessins d’enfants. The first author was supported in part by the Natural Sciences and Engineering Research Council of Canada, Riemann–Hilbert problem

Аннотация: A discrete version of the classical Riemann-Hilbert problem is stated and solved. In particular, a Riemann-Hilbert problem is associated with every dessin d'enfants. It is shown how to compute the solution for a dessin that is a tree. This amounts to finding a Fuchsian differential equation satisfied by the local inverses of a ShabПоказать полностьюat polynomial. A universal annihilating operator for the inverses of a generic polynomial is produced. A classification is given for the plane trees that have a representation by Mobius transformations and for those that have a linear representation of dimension at most two. This yields an analogue for trees of Schwarz's classical list, that is, a list of the plane trees whose Riemann-Hilbert problem has a hypergeometric solution of order at most two.

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Издание

Журнал: ST PETERSBURG MATHEMATICAL JOURNAL

Выпуск журнала: Vol. 19, Is. 6

Номера страниц: 1003-1014

ISSN журнала: 10610022

Место издания: Providence

Издатель: Amer Mathematical SOC

Персоны

  • Larusson F. (Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia)
  • Sadykov T. (Siberian Fed Univ, Dept Math & Comp Sci, Krasnoyarsk 660041, Russia)

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