Moduli spaces of Z/ kZ -constellations over 2

Let ρ: ℤ/kℤ → SL(2, C) be a representation of a finite abelian group and let Ogen ⊂ HOMZ(R(ℤ/kℤ),ℚ) be the space of generic stability conditions on the set of G-constellations. We provide a combinatorial description of all the chambers C ⊂ gen and prove that there are k! of them. Moreover, we introduce the notion of simple chamber and we show that, in order to know all toric G-constellations, it is enough to build all simple chambers. We also prove that there are k · 2k-2 simple chambers. Finally, we provide an explicit formula for the tautological bundles RC over the moduli spaces MC for all chambers C ⊂ Ogen which only depends upon the chamber stair which is a combinatorial object attached to the chamber C.