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

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.