Macdonald Polynomials and BGG reciprocity for current algebras

Matthew Bennett, Arkady Berenstein, Vyjayanthi Chari, Anton Khoroshkin, Sergey Loktev

Published 2012-07-10Version 1

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 $\lie{sl}_{n+1}$.