Cherednik–Orr conjecture on nonsymmetric Macdonald polynomials and PBW characters

Let ${\mathfrak g}$ be a simple Lie algebra and let $\la$ be an antidominant weight. Let $W_\la$ be the corresponding level one Demazure module, with extremal vector $w_\la$, viewed as a cyclic module for the current algebra ${\mathfrak g}\otimes\mathbb C[t]$. The PBW filtration induces a bigrading on the associated graded module, and define

$$\ch_{PBW} W_\la=\sum_{k,s\ge 0} q^kp^s\ch \{v\in F_s/F_{s-1},\, dv=kv\}.$$

Cherednik–Orr conjecture. Assume that $\la$ is an antidominant weight. Then

$$E_\la(x,q^{-1},\infty)=\left.\ch_{PBW} W_\la\right|_{p=q}.$$

This conjecture identifies the $t\to\infty$ limit of nonsymmetric Macdonald polynomials with the PBW-twisted character of a level one Demazure module. The paper proves the conjecture in several special cases; its general status is not resolved in the supplied text.