A bijection between Littlewood-Richardson tableaux and rigged configurations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A bijection between Littlewood-Richardson tableaux and rigged configurations

Authors:	A N Kirillov A Schilling M Shimozono

Institution:	(1) Department of Physics, Graduate School of Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

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 $V^{R_1} \otimes \cdots \otimes V^{R_L}$ .

Keywords:	, Littlewood-Richardson tableaux, rigged configurations, generalized Kostka polynomials,
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