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A bijection between Littlewood-Richardson tableaux and rigged configurations

Anatol N. Kirillov·Anne Schilling·Mark Shimozono
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Abstract

A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particle expression for the generalized Kostka polynomials, which are q-analogues of multiplicities in tensor products of irreducible general linear group modules indexed by rectangular partitions.

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Anatol N. Kirillov, Anne Schilling, Mark Shimozono. 1999-01-08. A bijection between Littlewood-Richardson tableaux and rigged configurations. https://arxiv.org/abs/math/9901037

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