Using the fusion product of the representations of the Lie algebra $\mathfrak{ sl}_2$ we construct a set of the integrable highest weight $\hat{ \mathfrak{ sl}_2}$-modules $L^D$, depending on the vector $D\in\mathbb{ N}^{ k+1}$. In a special cases of $D$ our modules are isomorphic to the irreducible $\hat{ \mathfrak{ sl}_2}$-modules $L_{ i,k}$. We construct a basis of the $L^D$ and study the decomposition of $L^D$ on the irreducible components. We also write a formulas for the characters of $L^D$.
Categories: math.QA math.RT