A bijection between Littlewood-Richardson tableaux and rigged configurations

• A.N. Kirillov ^[1] ; A. Schilling ^[2] ; M. Shimozono ^[3]
  1. [1] Hokkaido University

     Hokkaido University

     Chūō-ku, Japón

     
  2. [2] University of Amsterdam

     University of Amsterdam

     Países Bajos

     
  3. [3] Virginia Tech - Wake Forest University

     Virginia Tech - Wake Forest University

     Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 8, Nº. 1, 2002, págs. 67-135
• Idioma: inglés
• DOI: 10.1007/s00029-002-8102-6
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• Resumen

  • 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 KλR(q) labeled by a partition λ and a sequence of rectangles R. The generalized Kostka polynomials are q-analogues of multiplicities of the irreducible GL(n,C) -module Vλ of highest weight λ in the tensor product VR1⊗⋯⊗VRL .