Resumen de Macdonald polynomials and BGG reciprocity for current algebras

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

• We study the category IgrIgr of graded representations with finite-dimensional graded pieces for the current algebra g⊗C[t]g⊗C[t] where gg is a simple Lie algebra. This category has many similarities with the category OO of modules for gg , and in this paper, we prove an analog of the famous BGG duality in the case of sln+1sln+1 .