, Volume 8, Issue 1, pp 67-135

A bijection between Littlewood-Richardson tableaux and rigged configurations

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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 \( V^{R_1} \otimes \cdots \otimes V^{R_L} \) .