01068nas a2200121   4500008004300000245007400043210007000117260001300187520067000200100002000870700002000890856003600910       2000                        en_Ud  00aMonodromy of certain Painlevé-VI transcendents and reflection groups0 aMonodromy of certain PainlevéVI transcendents and reflection gro  bSpringer3 aWe study the global analytic properties of the solutions of a particular family of Painleve\\\' VI equations with the parameters $\\\\beta=\\\\gamma=0$, $\\\\delta={1\\\\over2}$ and $\\\\alpha$ arbitrary. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group. This result is used to classify all the algebraic solutions of our Painleve\\\' VI equation.1 aDubrovin, Boris1 aMazzocco, Marta  uhttp://hdl.handle.net/1963/2882