$q$-characters of the tensor products in $\mathbf{sl}_2$-case

Let $\pi,\dots,\pi_n$ be irreducible finite-dimensional $\mathbf{sl}_2$-modules. Using the theory of representations of current algebras, we introduce several ways to construct a $q$-grading on $\pi_1\otimes\dots\otimes\pi_n$. We study the corresponding graded modules and prove that they are essentially the same.