BGG reciprocity for current algebras

By Vyjayanthi Chari, B. Ion. Compositio Mathematica, 2011

66 citations recorded by the source corpus.

In Bennett et al. [BGG reciprocity for current algebras, Adv. Math. 231 (2012), 276–305] it was conjectured 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1cb1533b03d189ddb3a8f9ff34f1e341e1c0fa66

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Citations in the corpus

Demazure Modules, Fusion Products and Q-Systems (2013, background): “ials of quiver varieties. The homological properties of the category are similar to those of the BGG category O for the simple Lie algebra. This similarity has been explored to some extent in [3] and [4] and leads to connections with symmetric functions and Macdonald polynomials. The subject also ha”
Affine highest weight categories and affine quasihereditary algebras (2014, background): “e algebra. This Lie algebra has a natural Z≥0-grading [10, §2.1]. Let C be the category of ﬁnitely generated graded Cg-modules. It is easy to check, using the description of the projective modules in [10], that C is a graded Noetherian Laurentian category, with qbeing the degree shift by a0 (we have”