SPECIALIZATION OF NONSYMMETRIC MACDONALD POLYNOMIALS AT t = ∞ AND DEMAZURE SUBMODULES OF LEVEL-ZERO EXTREMAL WEIGHT MODULES.

In this paper, we give a representation-theoretic interpretation of the specialization Ew◦λ(q,∞) of the nonsymmetric Macdonald polynomial Ew◦λ(q, t) at t = ∞ in terms of the Demazure submodule Vw◦- (λ) of the level-zero extremal weight module V (λ) over a quantum affine algebra of an arbitrary untwisted type. Here, λ is a dominant integral weight, and w◦ denotes the longest element in the finite Weyl group W. Also, for each x ∈ W, we obtain a combinatorial formula for the specialization Exλ(q,∞) at t = ∞ of the nonsymmetric Macdonald polynomial Exλ(q, t) and also a combinatorical formula for the graded character gch Vx- (λ) of the Demazure submodule Vx- (λ) of V (λ). Both of these formulas are described in terms of quantum Lakshmibai-Seshadri paths of shape λ. [ABSTRACT FROM AUTHOR]