Macdonald Polynomials and BGG reciprocity for current algebras

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

References in corpus (6)

• Current algebras, highest weight categories and quivers
• BGG reciprocity for current algebras
• Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas
• Proof of the combinatorial Kirillov-Reshetikhin conjecture
• Loewy series of Weyl modules and the Poincaré polynomials of quiver varieties
• Weyl modules, Demazure modules and finite crystals for non-simply laced type

Cited by in corpus (2)

• Highest weight categories and Macdonald polynomials
• Rogers-Ramanujan type identities and Nil-DAHA