A bijection between Littlewood-Richardson tableaux and rigged configurations

1999/01/08 by Anatol N. Kirillov, Anne Schilling, Mark Shimozono
Mathematics · #math.CO #math.QA #msc:05A19 #msc:05A15

paper · pdf

published as Selecta Mathematica, N.S., 8 (2002) 67-135 · 66 pages, AMS-LaTeX, requires xy.sty and related files

arxiv created 1999/01/08 · arxiv updated 2009/11/30

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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