Macdonald Polynomials and BGG reciprocity for current algebras

We study the category of graded representations with finite–dimensional graded pieces for the current algebra associated to a simple Lie algebra. This category has many similarities with the category $\mathcal{O}$ of modules for $\lie g$ and in this paper, we use the combinatorics of Macdonald polynomials to prove an analogue of the famous BGG duality in the case of $\text{lie}{sl}_{n+1}$.