Resumen de A bijection between Littlewood-Richardson tableaux and rigged configurations

A.N. Kirillov, A. Schilling, M. Shimozono

• 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 .