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.
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