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A UNIFORM MODEL FOR KIRILLOV–RESHETIKHIN CRYSTALS III: NONSYMMETRICMACDONALD POLYNOMIALS AT t = 0 AND DEMAZURE CHARACTERS

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Abstract

We establish the equality of the specialization E wλ (x ; q; 0) of the nonsymmetric Macdonald polynomial E wλ (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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Authors and Affiliations

  1. Departament of Mathematics and Statistics, State University of New York at Albany, Albany, NY, 12222, USA

    C. LENART

  2. Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-ku, Tokyo, 152-8551, Japan

    S. NAITO

  3. Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan

    D. SAGAKI

  4. Department of Mathematics, University of California, One Shields Avenue, Davis, CA, 95616-8633, USA

    A. SCHILLING

  5. Department of Mathematics, MC 0151, 460 McBryde Hall, Virginia Tech, 225 Stanger St., Blacksburg, VA, 24061, USA

    M. SHIMOZONO

Authors
  1. C. LENART
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  2. S. NAITO
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  3. D. SAGAKI
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  4. A. SCHILLING
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  5. M. SHIMOZONO
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Correspondence to A. SCHILLING.

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LENART, C., NAITO, S., SAGAKI, D. et al. A UNIFORM MODEL FOR KIRILLOV–RESHETIKHIN CRYSTALS III: NONSYMMETRICMACDONALD POLYNOMIALS AT t = 0 AND DEMAZURE CHARACTERS. Transformation Groups 22, 1041–1079 (2017). https://doi.org/10.1007/s00031-017-9421-1

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  • DOI: https://doi.org/10.1007/s00031-017-9421-1

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