Transformation Groups

, Volume 22, Issue 4, pp 1041–1079 | Cite as


  • S. NAITO
  • A. SCHILLINGEmail author


We establish the equality of the specialization E (x ; q; 0) of the nonsymmetric Macdonald polynomial E (x ; q; t) at t = 0 with the graded character gch U w + (λ) of a certain Demazure-type submodule U w + (λ) of a tensor product of “single-column” Kirillov–Reshetikhin modules for an untwisted affine Lie algebra, where λ is a dominant integral weight and w is a (finite) Weyl group element; this generalizes our previous result, that is, the equality between the specialization P λ(x ; q; 0) of the symmetric Macdonald polynomial P λ(x ; q; t) at t = 0 and the graded character of a tensor product of single-column Kirillov–Reshetikhin modules. We also give two combinatorial formulas for the mentioned specialization of nonsymmetric Macdonald polynomials: one in terms of quantum Lakshmibai–Seshadri paths and the other in terms of the quantum alcove model.


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© Springer Science+Business Media New York 2017

Authors and Affiliations

    • 1
  • S. NAITO
    • 2
    • 3
    • 4
    Email author
    • 5
  1. 1.Departament of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA
  2. 2.Department of MathematicsTokyo Institute of TechnologyTokyoJapan
  3. 3.Institute of MathematicsUniversity of TsukubaTsukubaJapan
  4. 4.Department of MathematicsUniversity of CaliforniaDavisUSA
  5. 5.Department of Mathematics, MC 0151, 460 McBryde HallVirginia TechBlacksburgUSA

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