  This is the second of two articles (independent of each other) devoted to the
analysis of the path description of the states in su(2)_k WZW models. Here we
present a constructive derivation of the fermionic character at level k based
on these paths. The starting point is the expression of a path in terms of a
sequence of nonlocal (formal) operators acting on the vacuum ground-state path.
Within this framework, the key step is the construction of the level-k operator
sequences out of those at level-1 by the action of a new type of operators.
These actions of operators on operators turn out to have a path interpretation:
these paths are precisely the finitized RSOS paths related to the unitary
minimal models M(k+1,k+2). We thus unravel -- at the level of the path
representation of the states --, a direct factorization into a k=1 spinon part
times a RSOS factor. It is also pointed out that since there are two fermionic
forms describing these finite RSOS paths, the resulting fermionic su(2)_k
characters arise in two versions. Finally, the relation between the present
construction and the Nagoya spectral decomposition of the path space is
sketched.
