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 \( V^{R_1} \otimes \cdots \otimes V^{R_L} \).
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Kirillov, A., Schilling, A. & Shimozono, M. A bijection between Littlewood-Richardson tableaux and rigged configurations . Sel. math., New ser. 8, 67 (2002). https://doi.org/10.1007/s00029-002-8102-6
DOI: https://doi.org/10.1007/s00029-002-8102-6