We establish the equality of the specialization $E_{ w\lambda}(x;q,0)$ of the nonsymmetric Macdonald polynomial $E_{ w\lambda}(x;q,t)$ at $t=0$ with the graded character $\mathop{ \rm gch} U_{ w}^{ +}(\lambda)$ of a certain Demazure-type submodule $U_{ w}^{ +}(\lambda)$ of a tensor product of "single-column" Kirillov--Reshetikhin modules for an untwisted affine Lie algebra, where $\lambda$ 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 $P_{ \lambda}(x;q,0)$ of the symmetric Macdonald polynomial $P_{ \lambda}(x;q,t)$ 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 a nonsymmetric Macdonald polynomial: one in terms of quantum Lakshmibai-Seshadri paths and the other in terms of the quantum alcove model.
Categories: math.QA math.RT