A bijection between Littlewood-Richardson tableaux and rigged configurations

Abstract. We define a bijection from Littlewood-Richardson tableaux to rigged configurations and show that it preserves the appropriate statistics. This proves in particular a quasi-particle expression for the generalized Kostka polynomials $ K_{\lambda R}(q) $ labeled by a partition $ \lambda $ and a sequence of rectangles R. The generalized Kostka polynomials are q-analogues of multiplicities of the irreducible $ GL(n, \mathbb{C}) $-module $ V^\lambda $ of highest weight $ \lambda $ in the tensor product $ V^{R_1} \otimes \cdots \otimes V^{R_L} $.