Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2007

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 Shabat 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: Алгебра и анализ

Выпуск журнала: Т. 19, № 6

Номера страниц: 184-199

ISSN журнала: 02340852

Место издания: Санкт-Петербург

Издатель: Наука

• Larusson F. (School of Mathematical Sciences University of Adelaide)
• Sadykov T. (Siberian Federal University)

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