BGG reciprocity for current algebras

Vyjayanthi Chari, Bogdan Ion

Published 2013-07-04, updated 2014-08-20Version 2

It was conjectured by Bennett, Chari, and Manning that a BGG-type reciprocity holds for the category of graded representations with finite-dimensional graded components for the current algebra associated to a simple Lie algebra. We associate a current algebra to any indecomposable affine Lie algebra and show that, in this generality, the BGG reciprocity is true for the corresponding category of representations.