Fermionic characters and arbitrary highest-weight integrable sl̂_r+1-modules

This paper contains the generalization of the Feigin-Stoyanovsky construction to all integrable sl̂_r+1-modules. We give formulas for the q-characters of any highest-weight integrable module of sl̂_r+1 as a linear combination of the fermionic q-characters of the fusion products of a special set of integrable modules. The coefficients in the sum are the entries of the inverse matrix of generalized Kostka polynomials in q ^-1. We prove the conjecture of Feigin and Loktev regarding the q-multiplicities of irreducible modules in the graded tensor product of rectangular highest weight-modules in the case of sl̂_r+1. We also give the fermionic formulas for the q-characters of the (non-level-restricted) fusion products of rectangular highest-weight integrable sl̂_r+1.