THE PAINLEVE-III EQUATION AND THE IWASAWA DECOMPOSITION

For the third Painleve equation an explicit isomorphism between the mo nodromy data and the data of the approach of Dorfmeister-Pedit-Wu, bas ed on the Iwasawa decomposition of the loop groups, is established. As an application, this provides a simple algebraic way to calculate the monodromy data in terms of the Cauchy data at aero.