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arxiv: 1307.1440 · v2 · pith:AAQO3HOWnew · submitted 2013-07-04 · 🧮 math.RT · math.CO· math.QA

BGG reciprocity for current algebras

classification 🧮 math.RT math.COmath.QA
keywords algebracurrentreciprocitycategorygradedrepresentationsaffinealgebras
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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.

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