Path representation of suˆ(2)k states II: Operator construction of the fermionic character and spin-12-RSOS factorization

This is the second of two articles (independent of each other) devoted to the analysis of the path description of the states in suˆ(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 suˆ(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.