Inter-edge interactions and novel fixed points at a junction of quantum Hall line junctions

We show that novel fixed points (characterized by matrices which specify the splitting of the currents at the junction) can be accessed in a system which contains a junction of three quantum Hall line junctions. For such a junction of fractional quantum Hall edge states, we find that it is possible for both the flower (single droplet) and islands (three droplets) configurations to be stable in an intermediate region, for a range of values of the inter-edge repulsive interactions. A measurement of the tunneling conductance as a function of the gate voltage controlling inter-edge repulsions can give a clear experimental signal of this region.