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arXiv · 1207.2446

Macdonald Polynomials and BGG reciprocity for current algebras

Matthew Bennett·Arkady Berenstein·Vyjayanthi Chari·Anton Khoroshkin·Sergey Loktev
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Abstract

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

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Matthew Bennett, Arkady Berenstein, Vyjayanthi Chari, Anton Khoroshkin, Sergey Loktev. 2012-07-10. Macdonald Polynomials and BGG reciprocity for current algebras. https://arxiv.org/abs/1207.2446

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