Q-characters of the tensor products

Abstract

Let $π_1,...,π_n$ be an irreducible finite-dimensional $\mathfrak{sl}_2$-modules. Using the theory of the representations of the current algebras, we introduce a several ways to construct a $q$-grading on $π_1\otimes...\otimesπ_n$. We study the corresponding graded modules and prove, that they are essentially the same.

21 pages, with added references