ELLIPTIC ROOT SYSTEMS OF TYPE A1, A COMBINATORIAL STUDY

We consider some combinatorics of elliptic root systems of type a1. in particular, with respect to a fixed re ectable base, we give a precise description of the positive roots in terms of a positivity theorem. also the set of reduced words of the corresponding weyl group is precisely described. these then lead to a new characterization of the core of the corresponding lie algebra, namely we show that the core is generated by positive root spaces.