Infinite fusion products and sl̂₂ cosets

In this paper we study an approximation of tensor product of irreducible integrable sl̂₂ representations by infinite fusion products. This gives an approximation of the corresponding coset theories. As an application we represent characters of spaces of these theories as limits of certain restricted Kostka polynomials. This leads to the bosonic (which is known) and fermionic (which is new) formulas for the sl̂₂ branching functions.