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Working paper

Macdonald Polynomials and BGG reciprocity for current algebras

Bennett M., Berenstein A., Chari V., Khoroshkin A., Loktev S.
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 $\cal O$ 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 $\lie{sl}_{n+1}$.