  We extend the Schwinger boson large N treatment of the underscreened Kondo
model in a way that correctly captures the finite elastic phase shift in the
singular Fermi liquid. The new feature of the approach, is the introduction of
a flavor quantum number with K possible values, associated with the Schwinger
boson representation. The large N limit is taken maintaining the ratio k=K/N
fixed. This approach differs from previous approaches, in that we do not
explicitly enforce a constraint on the spin representation of the Schwinger
bosons. Instead, the energetics of the Kondo model cause the bosonic degrees of
freedom to ``self assemble'' into a ground-state in which the spins of K bosons
and N-K conduction electrons are antisymmetrically arranged into a Kondo
singlet. With this device, the large N limit can be taken, in such a way that a
fraction K/N of the Abrikosov Suhl resonance is immersed inside the Fermi sea.
We show how this method can be used to model the full energy dependence of the
singular Abrikosov Suhl resonance in the underscreened Kondo model and the
field-dependent magnetization.
