Graded Character for Fusion Products of Irreducible Modules and q -Littlewood-Richardson Polynomials of Type A ₂

We study a class of Chari-Venkatesh (CV) modules for the current algebra [Formula: see text]. Motivated by the Feigin-Loktev conjecture on fusion product modules, we focus on CV modules arising from the fusion product of two irreducible finite-dimensional [Formula: see text]-modules. We construct explicit filtrations, compute their graded characters, and provide a new proof of the conjecture asserting the independence of fusion products from the choice of parameters. In the process, we obtain an algebraic characterization of the dominant weights [Formula: see text] for which the Littlewood-Richardson coefficient [Formula: see text] is non-zero, and introduce a family of [Formula: see text]-analogues of these coefficients.