Arithmetic theory of symmetrizable split maximal Kac-Moody groups

In this thesis we present a reduction theory for the symmetrizable split maximal Kac-Moody groups. However there are many technical difficulties before one can even formulate a reduction theorem. Combining the two main approaches commonly seen in the literature we define a group, first over any field of characteristic zero and then on any commutative ring of characteristic zero. Then we prove a number of structural properties of the group such as representation in the highest weight modules, existence of a Tits system and an Iwasawa decomposition over ℝ and ℂ. Finally we arrive at reduction theory which can only hold for part of the group.Science, Faculty ofMathematics, Department ofGraduat