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Article

Macdonald Polynomials and BGG reciprocity for current algebras

Selecta Mathematica, New Series. 2014. No. 2. P. 585-607.
Benett 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 O of modules for 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 sl(n+1)