FUSION PRODUCTS OF slN SYMMETRIC POWER REPRESENTATIONS AND KOSTKA POLYNOMIALS

where Mλ,μ is a multiplicity space on which g acts trivially, of dimension Kλ,μ which can be computed from the Clebsch-Gordan coefficients or the Littlewood-Richardson rule. The Schur-Weyl duality concerns the case where μ = (1) for all i. In that case, there is an action of the symmetric group SN on the tensor product by permutation of factors, which centralizes the action of sln. In this case, Mλ,{1,...,1} ' Wλ is the irreducible Specht module of the symmetric group. In the case when μ = (μi) are single-part partitions, Mλ,μ is not an SN -module but its dimension is known to be the Kostka number Kλ,μ. Here, μ = (μ1, ..., μm), where without loss of generality we order μi ≥ μi+1. The Feigin-Loktev fusion product, inspired by the definition of the fusion action of the affine algebra ĝ on conformal blocks of WZW models in conformal field theory, is a g-equivariant grading on the tensor product