Occupation of a resonant level coupled to a chiral Luttinger liquid

We consider a resonant level coupled to a chiral Luttinger liquid which can be realized, e.g., at a fractional quantum Hall edge. We study the dependence of the occupation probability n of the level on its energy \epsilon for various values of the Luttinger-liquid parameter g. At g<1/2 a weakly coupled level shows a sharp jump in n(\epsilon) at the Fermi level. As the coupling is increased, the magnitude of the jump decreases until \sqrt{2g}, and then the discontinuity in n(\epsilon) disappears. We show that n(\epsilon) can be expressed in terms of the magnetization of a Kondo impurity as a function of magnetic field.