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.
Издание
Журнал: Алгебра и анализ
Выпуск журнала: Т. 19, № 6
Номера страниц: 184-199
ISSN журнала: 02340852
Место издания: Санкт-Петербург
Издатель: Наука
Персоны
- Larusson F. (School of Mathematical Sciences University of Adelaide)
- Sadykov T. (Siberian Federal University)
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