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BGG reciprocity for current algebras

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.

preprint2014arXivOpen access
Vyjayanthi ChariBogdan Ion
math.COmath.RTmath.QA
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Vyjayanthi ChariBogdan Ion

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